WISKUNDIGE GELETTERDHEID
Graad 11
NOG OEFENINGE
Omtrek, oppervlakte en volume : antwoorde

MATHEMATICAL LITERACY
Grade 11
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Perimeter, area and volume : answers

Antwoorde / Answers  1

$$\hspace*{6 mm}\mathrm{1.1\kern2mmLengte\ =\ L\ =\ 45\ mm, }$$ $$\hspace*{13 mm}\mathrm{breedte\ =\ B\ =\ 45\ mm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte =\ L\ X\ B \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 45\ \times\ 73\ mm^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 3\ 285\ mm^2 }$$

$$\hspace*{6 mm}\mathrm{1.2\kern2mmBasis\ =\ B\ =\ 56\ cm, }$$ $$\hspace*{13 mm}\mathrm{hoogte\ =\ H\ =\ 21\ cm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac12\times\ B\times\ H }$$

$$\hspace*{33 mm}\mathrm{=\ \frac12\times\ 56\times\ 21\ cm^2 }$$

$$\hspace*{33 mm}\mathrm{=\ 588\ cm^2 }$$

$$\hspace*{6 mm}\mathrm{1.3\kern2mmBasis\ =\ B\ =\ 45\ m, }$$ $$\hspace*{13 mm}\mathrm{hoogte\ =\ H\ =\ 22\ m, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac12\times\ B\times\ H \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ \frac12\times\ 45\times\ 22\ m^2 \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ 496\ m^2 }$$

$$\hspace*{6 mm}\mathrm{1.4\kern2mmSy\ =\ s\ =\ 72\ cm, }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ s\times\ s\ =\ s^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 72^2\ cm^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 5\ 184\ cm^2 }$$

$$\hspace*{6 mm}\mathrm{1.5\kern2mmBasis\ =\ B\ =\ 3,9\ m, }$$ $$\hspace*{13 mm}\mathrm{hoogte\ =\ H\ =\ 1,8\ m \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac12\times\ B\times\ H \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ \frac12\times\ 3,9\times\ 1,8\ cm^2 \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ 3,42\ m^2 }$$

$$\hspace*{6 mm}\mathrm{1.6\kern2mmBasis\ =\ B\ =\ 56\ m, }$$ $$\hspace*{13 mm}\mathrm{hoogte\ =\ H\ =\ 46,4\ m \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac12\times\ B\times\ H \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ \frac12\times\ 56\times\ 46,4\ m^2 \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ 1\ 299,2\ m^2 }$$

$$\hspace*{6 mm}\mathrm{1.7\kern2mmRadius\ =\ r\ =\ 14,7\ cm, }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \pi\ r^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ \pi\times\ 14,7^2\ cm^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 678,867\ cm^2 }$$

$$\hspace*{6 mm}\mathrm{1.8\kern2mmMiddellyn\ =\ d\ =\ 3,14\ m, }$$
$$\hspace*{13 mm}\mathrm{radius\ =\ r\ =\ \frac{d}{2}\ =\ \frac{3,14}{2}\ =\ 1,57 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac{\pi\ \times\ d^2}{4} \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ \frac{\pi\ \times\ 3,14^2}{4}\ m^2 \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ 678,867\ m^2 }$$

$$\hspace*{6 mm}\mathrm{1.9\kern2mmEen\ reghoek\ sy\ is\ die\ basis }$$ $$\hspace*{13 mm}\mathrm{en\ die\ ander\ die\ hoogte. }$$ $$\hspace*{13 mm}\mathrm{Bereken\ die\ lengte\ van\ die\ tweede }$$ $$\hspace*{13 mm}\mathrm{reghoek\ sy\ deur\ Pythagoras }$$ $$\hspace*{13 mm}\mathrm{se\ stelling\ te\ gebruik. }$$

$$\hspace*{13 mm}\mathrm{Laat\ die\ skuinssy\ gelyk\ wees }$$ $$\hspace*{13 mm}\mathrm{aan\ a,\ een\ reghoek\ sy\ =\ b \kern30mm }$$ $$\hspace*{13 mm}\mathrm{en\ die\ ander\ =\ c. }$$

$$\hspace*{13 mm}\mathrm{a^2\ =\ b^2\ +\ c^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{2,6^2\ =\ 1^2\ +\ c^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{6,76\ ─\ 1\ =\ c^2 }\kern30mm$$ $$\hspace*{13 mm}\mathrm{5,76\ =\ c^2 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{c\ =\ \sqrt{5,76} \kern30mm }$$
$$\hspace*{13 mm}\mathrm{c\ =\ 2,4 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Basis\ =\ B\ =\ 1\ cm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{hoogte\ =\ H\ =\ 2,4\ cm \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac12\times\ L\ \times\ B \kern30mm }$$

$$\hspace*{34 mm}\mathrm{=\ \frac12\ 1\times\ 2,4\ cm^2 \kern30mm }$$

$$\hspace*{34 mm}\mathrm{=\ 1,2\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.1\kern2mmLength\ =\ L\ =\ 45\ mm, }$$ $$\hspace*{13 mm}\mathrm{breadth\ =\ B\ =\ 45\ mm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ L\times\ B \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 45\times\ 73\ mm^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 3\ 285\ mm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.2\kern2mmBase\ =\ B\ =\ 56\ cm, }$$ $$\hspace*{13 mm}\mathrm{height\ =\ H\ =\ 21\ cm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ \frac12\times\ B\times\ H \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac12\ 56\times\ 21\ cm^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 588\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.3\kern2mmBase\ =\ B\ =\ 45\ m, }$$ $$\hspace*{13 mm}\mathrm{height\ =\ H\ =\ 22\ m, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ \frac12\times\ B\times\ H \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac12\ 45\times\ 22\ m^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 496\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.4\kern2mmSide\ =\ s\ =\ 72\ cm, }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ s\times\ s =\ s^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 72^2\ cm^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 5\ 184\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.5\kern2mmBase\ =\ B\ =\ 3,9\ m, }$$ $$\hspace*{13 mm}\mathrm{height\ =\ H\ =\ 1,8\ m, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ \frac12\times\ L\times\ B \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac12\ 3,9\times\ 1,8\ m^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 3,42\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.6\kern2mmBase\ =\ B\ =\ 56\ m, }$$ $$\hspace*{13 mm}\mathrm{height\ =\ H\ =\ 46,4\ m, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ \frac12\times\ L\times\ B \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac12\times\ 56\times\ 46,4\ m^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 1\ 299,2\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.7\kern2mmRadius\ =\ r\ =\ 14,7\ cm, }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ \pi\times\ r^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ \pi\times\ 14,7^2\ cm^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 678,867\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.8\kern2mmDiameter\ =\ d\ =\ 3,14\ m, }$$
$$\hspace*{13 mm}\mathrm{radius\ =\ r\ =\ \frac{d}{2}\ =\ \frac{3,14}{2}\ =\ 1,57\ m }$$

$$\hspace*{13 mm}\mathrm{Area\ =\ \frac{\pi\times\ d^2}{4} \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac{\pi\times\ 3,14^2}{4}\ m^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 678,867\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{1.9\kern2mmOne\ right-angled\ side\ is\ the\ base }$$ $$\hspace*{13 mm}\mathrm{and\ the\ other\ the\ height. }$$ $$\hspace*{13 mm}\mathrm{Calculate\ the\ length\ of\ the\ second\ }$$ $$\hspace*{13 mm}\mathrm{right-angled\ side\ by\ using\ the }$$ $$\hspace*{13 mm}\mathrm{theorem\ of\ Pythagoras. }$$

$$\hspace*{13 mm}\mathrm{Let\ the\ hypotenuse\ be\ equal\ to\ a, }$$ $$\hspace*{13 mm}\mathrm{one\ right-angled\ side\ =\ b }$$ $$\hspace*{13 mm}\mathrm{and\ the\ other\ =\ c. }$$

$$\hspace*{13 mm}\mathrm{a^2\ =\ b^2\ +\ c^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{2,6^2\ =\ 1^2\ +\ c^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{6,76\ ─\ 1\ =\ c^2 }\kern30mm$$ $$\hspace*{13 mm}\mathrm{5,76\ =\ c^2 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{c\ =\ \sqrt{5,76} \kern30mm }$$
$$\hspace*{13 mm}\mathrm{c\ =\ 2,4 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Base\ =\ B\ =\ 1\ cm, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{height\ =\ H\ =\ 2,4\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Area\ =\ \frac12\times\ L\times\ B \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ \frac12\ 1\times\ 2,4\ cm^2 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{=\ 1,2\ cm^2 \kern30mm }$$

Antwoorde / Answers  2

$$\hspace*{13 mm}\mathrm{Bereken\ die\ oppervlakte\ van\ die }$$ $$\hspace*{13 mm}\mathrm{muur\ en\ die\ oppervlakte\ van\ }$$ $$\hspace*{13 mm}\mathrm{1\ steen\ en\ gebruik\ dan \kern30mm }$$
$$\hspace*{13 mm}\mathrm{die\ gegewe\ formule\ : }$$
$$\hspace*{13 mm}\mathrm{Bereken\ al\ die\ oppervlaktes\ in\ m^2 }$$ $$\hspace*{13 mm}\mathrm{Muur\ is\ 6,60\ m\ lank\ =\ L\ en \kern30mm }$$ $$\hspace*{13 mm}\mathrm{muur\ is\ 3,25\ m\ hoog\ =\ B \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ L\times\ B \kern30mm }$$ $$\hspace*{34 mm}\mathrm{=\ 6,60\times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{34 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Steen\ is\ 30\ cm\ lank\ =\ L\ en \kern30mm }$$ $$\hspace*{13 mm}\mathrm{50\ mm\ hoog\ =\ B \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Steen\ :\ L\ =\ 30\ cm\ =\ \frac{30}{100}\ m \kern30mm }$$

$$\hspace*{47 mm}\mathrm{=\ 0,03\ m }$$
$$\hspace*{13 mm}\mathrm{Steen\ :\ B\ =\ 50\ mm\ =\ \frac{50}{1\ 000}\ m \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 0,05\ m \kern30mm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ steen\ =\ L\times\ B }$$ $$\hspace*{44 mm}\mathrm{=\ 0,3\times\ 0,05\ m^2 \kern30mm }$$
$$\hspace*{44 mm}\mathrm{=\ 0,015\ m^2 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Aantal\ stene\ =\ \frac{Oppervlakte\ muur}{Oppervlakte\ steen} }$$

$$\hspace*{35 mm}\mathrm{=\ \frac{21,45}{0,015} }$$

$$\hspace*{35 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{Maar\ die\ muur\ is\ 2\ stene\ breed, \kern20mm }$$ $$\hspace*{13 mm}\mathrm{en\ dus\ is\ die\ totale\ aantal\ stene \kern20mm }$$ $$\hspace*{13 mm}\mathrm{tweemaal\ 1\ 430\ d.w.s.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Bereken\ al\ die\ oppervlaktes\ in\ cm^2 }$$ $$\hspace*{13 mm}\mathrm{Muur\ is\ 6,60\ m\ lank\ =\ L \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 6,60\ \times\ 100\ cm^2 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 660\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{muur\ is\ 3,25\ m\ hoog\ =\ B \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 3,25\ \times\ 100\ cm \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 325\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ muur =\ L\times\ B \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 660\ \times\ 325\ cm^2 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 214\ 500\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Steen\ is\ 30\ cm\ lank\ =\ L\ en \kern30mm }$$ $$\hspace*{13 mm}\mathrm{steen\ is\ 50\ mm\ hoog\ =\ B \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 5\ cm \kern30mm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ steen\ =\ L\times\ B }$$ $$\hspace*{44 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$
$$\hspace*{44 mm}\mathrm{=\ 150\ cm^2 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Aantal\ stene\ =\ \frac{Oppervlakte\ muur}{Oppervlakte\ steen} }$$

$$\hspace*{35 mm}\mathrm{=\ \frac{214\ 500}{150} }$$

$$\hspace*{35 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{Maar\ die\ muur\ is\ 2\ stene\ breed, \kern20mm }$$ $$\hspace*{13 mm}\mathrm{en\ dus\ is\ die\ totale\ aantal\ stene \kern20mm }$$ $$\hspace*{13 mm}\mathrm{tweemaal\ 1\ 430\ d.w.s.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Bereken\ die\ oppervlakte\ van\ die }$$ $$\hspace*{13 mm}\mathrm{muur\ in\ m^2\ en\ die\ van\ die\ steen }$$ $$\hspace*{13 mm}\mathrm{in\ cm^2.\ Skakel\ dan\ die \kern30mm }$$ $$\hspace*{13 mm}\mathrm{cm^2\ om\ na\ m^2. \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ muur =\ L\times\ B \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 6,60\ \times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Steen\ is\ 50\ mm\ hoog\ =\ B \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 5\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ steen =\ L\times\ B \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 150\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Skakel\ nou\ cm^2\ om\ na\ m^2 }$$
$$\hspace*{13 mm}\mathrm{150\ cm^2\ =\ \frac{150}{100\ \times\ 100}\ m^2 }$$

$$\hspace*{28 mm}\mathrm{=\ 0,015\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Bereken\ nou\ die\ aantal\ stene\ met }$$ $$\hspace*{13 mm}\mathrm{die\ gegewe\ formule. }$$ $$\hspace*{13 mm}\mathrm{Aantal\ stene\ =\ \frac{Oppervlakte\ muur}{Oppervlakte\ steen} }$$

$$\hspace*{35 mm}\mathrm{=\ \frac{21,45}{0,015} }$$

$$\hspace*{35 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{Maar\ die\ muur\ is\ 2\ stene\ breed, \kern20mm }$$ $$\hspace*{13 mm}\mathrm{en\ dus\ is\ die\ totale\ aantal\ stene \kern20mm }$$ $$\hspace*{13 mm}\mathrm{tweemaal\ 1\ 430\ d.w.s.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Bereken\ die\ oppervlakte\ van\ die }$$ $$\hspace*{13 mm}\mathrm{muur\ in\ m^2\ en\ die\ van\ die\ steen }$$ $$\hspace*{13 mm}\mathrm{in\ cm^2.\ Skakel\ dan\ die \kern30mm }$$ $$\hspace*{13 mm}\mathrm{m^2\ om\ na\ cm^2. \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Oppervlakte\ muur =\ L\times\ B \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 6,60\ \times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Steen\ is\ 50\ mm\ hoog\ =\ B \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 5\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ steen =\ L\times\ B \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 150\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Skakel\ nou\ m^2\ om\ na\ cm^2 }$$
$$\hspace*{13 mm}\mathrm{21,45\ m^2\ =\ 21,45\ \times\ (100\ \times\ 100)\ cm^2 }$$ $$\hspace*{30 mm}\mathrm{=\ 214\ 500\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Bereken\ nou\ die\ aantal\ stene\ met }$$ $$\hspace*{13 mm}\mathrm{die\ gegewe\ formule. }$$ $$\hspace*{13 mm}\mathrm{Aantal\ stene\ =\ \frac{Oppervlakte\ muur}{Oppervlakte\ steen} }$$

$$\hspace*{35 mm}\mathrm{=\ \frac{214\ 500}{150} }$$

$$\hspace*{35 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{Maar\ die\ muur\ is\ 2\ stene\ breed, \kern20mm }$$ $$\hspace*{13 mm}\mathrm{en\ dus\ is\ die\ totale\ aantal\ stene \kern20mm }$$ $$\hspace*{13 mm}\mathrm{tweemaal\ 1\ 430\ d.w.s.\ 2\ 860 }$$

$$\hspace*{13 mm}\mathrm{Calculate\ the\ area\ of\ the }$$ $$\hspace*{13 mm}\mathrm{wall\ and\ the\ area\ of\ }$$ $$\hspace*{13 mm}\mathrm{1\ brick\ and\ then\ use\ the \kern30mm }$$
$$\hspace*{13 mm}\mathrm{given\ formula\ : }$$
$$\hspace*{13 mm}\mathrm{Calculate\ all\ the\ areas\ in\ m^2 }$$ $$\hspace*{13 mm}\mathrm{Wall\ is\ 6,60\ m\ long\ =\ L\ and \kern30mm }$$ $$\hspace*{13 mm}\mathrm{wall\ is\ 3,25\ m\ high\ =\ B \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ =\ L\times\ B \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 6,60\times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Brick\ is\ 30\ cm\ long\ =\ L\ and \kern30mm }$$ $$\hspace*{13 mm}\mathrm{50\ mm\ high\ =\ B \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Brick\ :\ L\ =\ 30\ cm\ =\ \frac{30}{100}\ m \kern30mm }$$

$$\hspace*{46 mm}\mathrm{=\ 0,03\ m }$$
$$\hspace*{13 mm}\mathrm{Brick\ :\ B\ =\ 50\ mm\ =\ \frac{50}{1\ 000}\ m \kern30mm }$$

$$\hspace*{47 mm}\mathrm{=\ 0,05\ m \kern30mm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ brick\ =\ L\times\ B }$$ $$\hspace*{36 mm}\mathrm{=\ 0,3\times\ 0,05\ m^2 \kern30mm }$$
$$\hspace*{36 mm}\mathrm{=\ 0,015\ m^2 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Number\ bricks\ =\ \frac{Area\ wall}{Area\ brick} }$$

$$\hspace*{38 mm}\mathrm{=\ \frac{21,45}{0,015} }$$

$$\hspace*{38 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{But\ the\ wall\ is\ 2\ bricks\ broad,\ and \kern20mm }$$ $$\hspace*{13 mm}\mathrm{thus\ the\ total\ number\ of\ bricks\ is \kern20mm }$$ $$\hspace*{13 mm}\mathrm{twice\ 1\ 430\ i.e.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Calculate\ all\ the\ areas\ in\ cm^2 }$$ $$\hspace*{13 mm}\mathrm{Wall\ is\ 6,60\ m\ long\ =\ L \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 6,60\ \times\ 100\ cm^2 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 660\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{wall\ is\ 3,25\ m\ high\ =\ B \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 3,25\ \times\ 100\ cm \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 325\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ of\ wall =\ L\times\ B \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 660\ \times\ 325\ cm^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 214\ 500\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Brick\ is\ 30\ cm\ long\ =\ L\ and \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Brick\ is\ 50\ mm\ high\ =\ B \kern30mm }$$

$$\hspace*{46 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{46 mm}\mathrm{=\ 5\ cm \kern30mm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ brick\ =\ L\times\ B }$$ $$\hspace*{36 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$
$$\hspace*{36 mm}\mathrm{=\ 150\ cm^2 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Number\ of\ bricks\ =\ \frac{Area\ of\ wall}{Area\ of\ brick} }$$

$$\hspace*{42 mm}\mathrm{=\ \frac{214\ 500}{150} }$$

$$\hspace*{42 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{But\ the\ wall\ is\ 2\ bricks\ broad,\ and \kern20mm }$$ $$\hspace*{13 mm}\mathrm{thus\ the\ total\ number\ of\ bricks\ is \kern20mm }$$ $$\hspace*{13 mm}\mathrm{twice\ 1\ 430\ i.e.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Calculate\ the\ area\ of\ the }$$ $$\hspace*{13 mm}\mathrm{wall\ in\ m^2\ and\ that\ of\ the\ brick }$$ $$\hspace*{13 mm}\mathrm{in\ cm^2.\ Then\ convert\ the \kern30mm }$$ $$\hspace*{13 mm}\mathrm{cm^2\ to\ m^2. \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ of\ wall =\ L\times\ B \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 6,60\ \times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Brick\ is\ 50\ mm\ high\ =\ B \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 5\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ brick =\ L\times\ B \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 150\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Now\ convert\ cm^2\ to\ m^2 }$$
$$\hspace*{13 mm}\mathrm{150\ cm^2\ =\ \frac{150}{100\ \times\ 100}\ m^2 }$$

$$\hspace*{28 mm}\mathrm{=\ 0,015\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Now\ calculate\ the\ number\ of\ bricks }$$ $$\hspace*{13 mm}\mathrm{using\ the\ given\ formula. }$$ $$\hspace*{13 mm}\mathrm{Number\ of\ bricks\ =\ \frac{Area\ of\ wall}{Area\ of\ brick} }$$

$$\hspace*{43 mm}\mathrm{=\ \frac{21,45}{0,015} }$$

$$\hspace*{43 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{But\ the\ wall\ is\ 2\ bricks\ broad,\ and \kern20mm }$$ $$\hspace*{13 mm}\mathrm{thus\ the\ total\ number\ of\ bricks\ is \kern20mm }$$ $$\hspace*{13 mm}\mathrm{twice\ 1\ 430\ i.e.\ 2\ 860 }$$

$$\hspace*{38 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Calculate\ thr\ area\ of\ the }$$ $$\hspace*{13 mm}\mathrm{wall\ in\ m^2\ and\ that\ of\ the\ brick }$$ $$\hspace*{13 mm}\mathrm{in\ cm^2.\ Then\ convert\ the \kern30mm }$$ $$\hspace*{13 mm}\mathrm{m^2\ to\ cm^2. \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Area\ of\ wall\ =\ L\times\ B \kern30mm }$$ $$\hspace*{34 mm}\mathrm{=\ 6,60\ \times\ 3,25\ m^2 \kern30mm }$$ $$\hspace*{34 mm}\mathrm{=\ 21,45\ m^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Brick\ is\ 50\ mm\ high\ =\ B \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ \frac{50}{10}\ cm \kern30mm }$$

$$\hspace*{48 mm}\mathrm{=\ 5\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ brick\ =\ L\times\ B \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 30\ \times\ 5\ cm^2 \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 150\ cm^2 \kern50mm }$$

$$\hspace*{13 mm}\mathrm{Now\ convert\ m^2\ to\ cm^2 }$$
$$\hspace*{13 mm}\mathrm{21,45\ m^2\ =\ 21,45\ \times\ (100\ \times\ 100)\ cm^2 }$$ $$\hspace*{30 mm}\mathrm{=\ 214\ 500\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{The\ number\ of\ bricks\ can\ now\ be }$$ $$\hspace*{13 mm}\mathrm{calculated\ by\ using\ the\ given\ formula }$$ $$\hspace*{13 mm}\mathrm{Number\ bricks\ =\ \frac{Area\ of\ wall}{Area\ of\ brick} }$$

$$\hspace*{38 mm}\mathrm{=\ \frac{214\ 500}{150} }$$

$$\hspace*{38 mm}\mathrm{=\ 1\ 430 }$$
$$\hspace*{13 mm}\mathrm{But\ the\ wall\ is\ 2\ bricks\ broad,\ and \kern20mm }$$ $$\hspace*{13 mm}\mathrm{thus\ the\ total\ number\ of\ bricks\ is \kern20mm }$$ $$\hspace*{13 mm}\mathrm{twice\ 1\ 430\ i.e.\ 2\ 860 }$$

Antwoorde / Answers  3

$$\hspace*{6 mm}\mathrm{3.1\kern2mmOppervlakte\ van\ vierkant\ =\ sy^2 }$$ $$\hspace*{24 mm}\mathrm{552,25\ =\ sy^2 \kern30mm }$$ $$\hspace*{34 mm}\mathrm{s\ =\ \sqrt{552,25} \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 23,5 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Vierkant\ se\ sy\ =\ 23,5\ m \kern30mm}$$
$$\hspace*{13 mm}\mathrm{Omtrek\ van\ vierkant\ =\ 4\ \times\ sy }$$ $$\hspace*{47 mm}\mathrm{=\ 4\ \times\ 23,5\ m \kern30mm }$$ $$\hspace*{47 mm}\mathrm{=\ 94\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.2\kern2mmOppervlakte\ reghoek\ =\ L\ \times\ B }$$ $$\hspace*{20 mm}\mathrm{L\ \times\ B\ =\ oppervlakte\ reghoek \kern30mm }$$ $$\hspace*{15 mm}\mathrm{L\ \times\ 3,45\ =\ 20,769 \kern30mm }$$

$$\hspace*{28 mm}\mathrm{L\ =\ \frac{20,769}{3,45} \kern30mm }$$

$$\hspace*{32 mm}\mathrm{=\ 6,02 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Lengte\ van\ reghoek\ =\ 6,02\ m \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Omtrek\ reghoek\ =\ 2(L\ +\ B) \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 2(6,02\ +\ 3,45)\ m \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 18,94\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.3\kern2mmOppervlakte\ van\ driehoek\ =\ \frac12BH }$$ $$\hspace*{20 mm}\mathrm{\frac12BHL\ =\ oppervlakte\ driehoek \kern30mm }$$

$$\hspace*{28 mm}\mathrm{\frac12\ \times\ 28,4\ \times\ H\ =\ 249,92 \kern30mm }$$

$$\hspace*{40 mm}\mathrm{H\ =\ \frac{2\ \times\ 249,92}{28,4} \kern30mm }$$

$$\hspace*{45 mm}\mathrm{=\ 17,6 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Hoogte\ van\ friehoek =\ 17,6\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.4\kern2mmOppervlakte\ van\ driehoek\ =\ \frac12BH }$$ $$\hspace*{20 mm}\mathrm{\frac12BHL\ =\ oppervlakte\ driehoek \kern30mm }$$

$$\hspace*{28 mm}\mathrm{\frac12\ \times\ B\ \times\ 1,26\ =\ 0,4095 \kern30mm }$$

$$\hspace*{40 mm}\mathrm{H\ =\ \frac{2\ \times\ 0,4095}{1,26} \kern30mm }$$

$$\hspace*{45 mm}\mathrm{=\ 0,65 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Basis\ van\ friehoek =\ 0,65\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.5\kern2mmOppervlakte\ van\ sirkel\ =\ \pi\ r^2 }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ oppervlakte\ sirkel \kern30mm }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ 124,690 \kern30mm }$$

$$\hspace*{31 mm}\mathrm{r^2\ =\ \frac{124,690}{\pi} \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r^2\ =\ 39,69005971 \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r\ =\ \sqrt{39,69005971} \kern30mm }$$
$$\hspace*{34 mm}\mathrm{=\ 6,300\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Deursnit\ van\ sirkel\ =\ D\ =\ 2\ r \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 2\ \times\ 6,300\ cm \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 12,600\ cm \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Omtrek\ van\ sirkel\ =\ 2\ \pi\ r \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 2\ \times\ \pi\ \times\ 6,3\ cm \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 39,584\ cm \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac{\pi\ \times\ D^2}{4} \kern30mm }$$

$$\hspace*{19 mm}\mathrm{\frac{\pi\ \times\ D^2}{4}\ =\ 124,690 \kern30mm }$$

$$\hspace*{27 mm}\mathrm{D^2\ =\ \frac{4\ \times\ 124,690}{\pi} \kern30mm }$$

$$\hspace*{33 mm}\mathrm{=\ 158,7602388 \kern30mm }$$
$$\hspace*{28 mm}\mathrm{D\ =\ \sqrt{158,7602388} \kern30mm }$$ $$\hspace*{32 mm}\mathrm{=\ 12,600 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Middellyn\ van\ sirkel\ =\ 12,600\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Omtrek\ van\ sirkel\ =\ \pi\ D \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ \pi\ \times\ 12,600\ cm \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ 39,584\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.6\kern2mmOppervlakte\ van\ sirkel\ =\ \pi\ r^2 }$$ $$\hspace*{22 mm}\mathrm{\pi\ r^2\ =\ oppervlakte\ van\ sirkel \kern30mm }$$ $$\hspace*{22 mm}\mathrm{\pi\ r^2\ =\ 3\ 848,45 \kern30mm }$$

$$\hspace*{25 mm}\mathrm{r^2\ =\ \frac{3\ 848,45}{\pi} \kern30mm }$$
$$\hspace*{25 mm}\mathrm{r^2\ =\ 1\ 224,999681 \kern30mm }$$
$$\hspace*{27 mm}\mathrm{r\ =\ \sqrt{1\ 224,999681} \kern30mm }$$
$$\hspace*{30 mm}\mathrm{=\ 34,99999545\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Radius\ van\ sirkel\ =\ 35,000\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Omtrek\ sirkel\ =\ 2\ \pi\ r \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 2\ \times\ \pi\ \times\ 35,000 \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 219,911\ cm \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ =\ \frac{\pi\ \times\ D^2}{4} \kern30mm }$$

$$\hspace*{20 mm}\mathrm{\frac{\pi\ \times\ D^2}{4}\ =\ 3\ 848,45 \kern30mm }$$

$$\hspace*{28 mm}\mathrm{D^2\ =\ \frac{4\ \times\ 3\ 848,45}{\pi} \kern30mm }$$

$$\hspace*{34 mm}\mathrm{=\ 4\ 899,998726 \kern30mm }$$
$$\hspace*{29 mm}\mathrm{D\ =\ \sqrt{4\ 899,998726} \kern30mm }$$ $$\hspace*{34 mm}\mathrm{=\ 69,9999909 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Middellyn\ van\ sirkel\ =\ 70,000\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Radius\ van\ sirkel\ =\ D\ \div\ 2 \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ 70\ \div\ 2 \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ 35\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Omtrek\ van\ sirkel\ =\ \pi\ D \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ \pi\ \times\ 70,000\ cm \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 219,911\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.1\kern2mmArea\ of\ square\ =\ side^2 }$$ $$\hspace*{25 mm}\mathrm{552,25\ =\ side^2 \kern30mm }$$ $$\hspace*{34 mm}\mathrm{s\ =\ \sqrt{552,25} \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 23,5 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Side\ of\ square\ =\ 23,5\ m }$$
$$\hspace*{13 mm}\mathrm{Perimeter\ square\ =\ 4\ \times\ side }$$ $$\hspace*{43 mm}\mathrm{=\ 4\ \times\ 23,5\ m \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 94\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.2\kern2mmArea\ rectangle\ =\ L\ \times\ B }$$ $$\hspace*{20 mm}\mathrm{L\ \times\ B\ =\ area\ of\ rectangle \kern30mm }$$ $$\hspace*{15 mm}\mathrm{L\ \times\ 3,45\ =\ 20,769 \kern30mm }$$

$$\hspace*{28 mm}\mathrm{L\ =\ \frac{20,769}{3,45} \kern30mm }$$

$$\hspace*{32 mm}\mathrm{=\ 6,02 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Length\ of\ rectangle\ =\ 6,02\ m \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Perimeter\ =\ 2(L\ +\ B) \kern30mm }$$ $$\hspace*{31 mm}\mathrm{=\ 2(6,02\ +\ 3,45)\ m \kern30mm }$$ $$\hspace*{31 mm}\mathrm{=\ 18,94\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.3\kern2mmArea\ of\ triangle\ =\ \frac12BH }$$ $$\hspace*{20 mm}\mathrm{\frac12BHL\ =\ area\ of\ triangle \kern30mm }$$

$$\hspace*{15 mm}\mathrm{\frac12\ \times\ 28,4\ \times\ H\ =\ 249,92 \kern30mm }$$

$$\hspace*{37 mm}\mathrm{H\ =\ \frac{2\ \times\ 249,92}{28,4} \kern30mm }$$

$$\hspace*{42 mm}\mathrm{=\ 17,6 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Height\ of\ triangle =\ 17,6\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.4\kern2mmArea\ of\ triangle\ =\ \frac12BH }$$ $$\hspace*{20 mm}\mathrm{\frac12BHL\ =\ area\ of\ triangle \kern30mm }$$

$$\hspace*{15 mm}\mathrm{\frac12\ \times\ B\ \times\ 1,26\ =\ 0,4095 \kern30mm }$$

$$\hspace*{37 mm}\mathrm{H\ =\ \frac{2\ \times\ 0,4095}{1,26} \kern30mm }$$

$$\hspace*{42 mm}\mathrm{=\ 0,65 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Base\ of\ triangle =\ 0,65\ m \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.5\kern2mmArea\ of\ circle\ =\ \pi\ r^2 }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ area\ of\ circle \kern30mm }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ 124,690 \kern30mm }$$

$$\hspace*{31 mm}\mathrm{r^2\ =\ \frac{124,690}{\pi} \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r^2\ =\ 39,69005971 \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r\ =\ \sqrt{39,69005971} \kern30mm }$$
$$\hspace*{34 mm}\mathrm{=\ 6,300\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Diameter\ of\ circle\ =\ D\ =\ 2\ r \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 2\ \times\ 6,300\ cm \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 12,600\ cm \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Circumference\ of\ circle\ =\ 2\ \pi\ r \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 2\ \times\ \pi\ \times\ 6,3\ cm \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 39,584\ cm \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Area\ =\ \frac{\pi\ \times\ D^2}{4} \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\frac{\pi\ \times\ D^2}{4}\ =\ 124,690 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{D^2\ =\ \frac{4\ \times\ 124,690}{\pi} \kern30mm }$$

$$\hspace*{28 mm}\mathrm{=\ 158,7602388 \kern30mm }$$
$$\hspace*{23 mm}\mathrm{D\ =\ \sqrt{158,7602388} \kern30mm }$$ $$\hspace*{28 mm}\mathrm{=\ 12,600 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Diameter\ of\ circle\ =\ 12,600\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Circumference\ of\ circle\ =\ \pi\ D \kern30mm }$$ $$\hspace*{13 mm}\mathrm{=\ \pi\ \times\ 12,600\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{=\ 39,584\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{3.6\kern2mmArea\ of\ circle\ =\ \pi\ r^2 }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ area\ of\ circle \kern30mm }$$ $$\hspace*{28 mm}\mathrm{\pi\ r^2\ =\ 3\ 848,45 \kern30mm }$$

$$\hspace*{31 mm}\mathrm{r^2\ =\ \frac{3\ 848,45}{\pi} \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r^2\ =\ 1\ 224,999681 \kern30mm }$$
$$\hspace*{31 mm}\mathrm{r\ =\ \sqrt{1\ 224,999681} \kern30mm }$$
$$\hspace*{34 mm}\mathrm{=\ 34,99999545\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Radius\ of\ circle\ =\ 35,000\ cm \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Circumference\ of\ circle\ =\ 2\ \pi\ r \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 2\ \times\ \pi\ \times\ 35,000\ cm \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 219,911\ cm \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Area\ =\ \frac{\pi\ \times\ D^2}{4} \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\frac{\pi\ \times\ D^2}{4}\ =\ 3\ 848,45 \kern30mm }$$

$$\hspace*{22 mm}\mathrm{D^2\ =\ \frac{4\ \times\ 3\ 848,45}{\pi} \kern30mm }$$

$$\hspace*{28 mm}\mathrm{=\ 4\ 899,998726 \kern30mm }$$
$$\hspace*{23 mm}\mathrm{D\ =\ \sqrt{4\ 899,998726} \kern30mm }$$ $$\hspace*{28 mm}\mathrm{=\ 69,9999909 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Diameter\ of\ circle\ =\ 70,000\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Radius\ of\ circle\ =\ D\ \div\ 2 \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 70\ \div\ 2 \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 35\ cm \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Circumference\ of\ circle\ =\ \pi\ D \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ \pi\ \times\ 70,000\ cm \kern30mm }$$ $$\hspace*{42 mm}\mathrm{=\ 219,911\ cm \kern30mm }$$

Antwoorde / Answers  4

$$\hspace*{6 mm}\mathrm{4.1\kern2mmBO\ van\ kubus\ =\ 6s^2 }$$ $$\hspace*{37 mm}\mathrm{=\ 34^2\ mm^2 \kern30mm }$$ $$\hspace*{37 mm}\mathrm{=\ 1\ 156\ mm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ van\ kubus\ =\ s^3 \kern30mm }$$
$$\hspace*{44 mm}\mathrm{=\ 34^3\ mm^3 }$$
$$\hspace*{44 mm}\mathrm{=\ 39\ 304\ mm^3 }$$

$$\hspace*{6 mm}\mathrm{4.2\kern2mmBO\ van\ prisma\ =\ 2(B+H)L+2BH }$$ $$\hspace*{20 mm}\mathrm{=\ 2(40+24)\times65+2\times40\times24 }$$ $$\hspace*{20 mm}\mathrm{=\ 10\ 240\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ van\ prisma\ =\ LBH }$$ $$\hspace*{30 mm}\mathrm{V\ =\ LBH }$$ $$\hspace*{34 mm}\mathrm{=\ 65\ \times\ 40\ \times\ 24\ cm^3 }$$ $$\hspace*{34 mm}\mathrm{=\ 62\ 400\ cm^3 }$$

$$\hspace*{6 mm}\mathrm{4.3\kern2mmLengte\ van\ silinder\ =\ hoogte\ =\ h }$$ $$\hspace*{40 mm}\mathrm{h\ =\ 450\ mm }$$ $$\hspace*{44 mm}\mathrm{=\ \frac{450}{10}\ cm }$$

$$\hspace*{44 mm}\mathrm{=\ 45\ cm \kern40mm }$$
$$\hspace*{13 mm}\mathrm{BO\ =\ \pi\ \times\ d\times(h\ +\ \frac12\times\ d)\ cm^2 }$$

$$\hspace*{13 mm}\mathrm{BO\ =\ \pi\times\ 6\times(45\ +\ \frac12\times6)\ cm^2 }$$ $$\hspace*{20 mm}\mathrm{=\ 904,779\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ van\ silinder\ =\ V \kern30mm }$$

$$\hspace*{37 mm}\mathrm{V\ =\ \frac{\pi\times\ D^2\times\ h}{4} \kern30mm }$$

$$\hspace*{41 mm}\mathrm{=\ \frac{\pi\times\ 6^2\times\ 45}{4} }$$

$$\hspace*{41 mm}\mathrm{=\ 1\ 272,345\ cm^3 }$$

$$\hspace*{37 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Lengte\ van\ silinder\ =\ height\ =\ h }$$ $$\hspace*{40 mm}\mathrm{h\ =\ 450\ mm }$$ $$\hspace*{44 mm}\mathrm{=\ \frac{450}{10}\ cm }$$

$$\hspace*{44 mm}\mathrm{=\ 45\ cm \kern40mm }$$
$$\hspace*{13 mm}\mathrm{Straal\ van\ silinder\ =\ r\ =\ \frac12\ D }$$
$$\hspace*{51 mm}\mathrm{=\ 3\ cm }$$

$$\hspace*{13 mm}\mathrm{BO\ =\ 2\pi\ r(r\ +\ h) }$$

$$\hspace*{13 mm}\mathrm{BO\ =\ 2\times\ \pi\times\ 3\times(3\ +\ 45)\ cm^2 }$$ $$\hspace*{20 mm}\mathrm{=\ 904,779\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ van\ silinder\ =\ V \kern30mm }$$

$$\hspace*{37 mm}\mathrm{V\ =\ \pi\ r^2\ h \kern30mm }$$
$$\hspace*{41 mm}\mathrm{=\ \pi\times\ 3^2\times 45\ cm^3 }$$
$$\hspace*{41 mm}\mathrm{=\ 1\ 272,345\ cm^3 }$$

$$\hspace*{6 mm}\mathrm{4.1\kern2mmSA\ of\ cube\ =\ 6s^2 }$$ $$\hspace*{33 mm}\mathrm{=\ 34^2\ mm^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 1\ 156\ mm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ of\ cube\ =\ s^3 \kern30mm }$$
$$\hspace*{40 mm}\mathrm{=\ 34^3\ mm^3 }$$
$$\hspace*{40 mm}\mathrm{=\ 39\ 304\ mm^3 }$$

$$\hspace*{6 mm}\mathrm{4.2\kern2mmSA\ of\ prism\ =\ 2(B| +\ H)L\ +\ 2BH }$$ $$\hspace*{20 mm}\mathrm{=\ 2(40+24)\times65+2\times40\times24 }$$ $$\hspace*{20 mm}\mathrm{=\ 10\ 240\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ of\ prism\ =\ LBH }$$ $$\hspace*{32 mm}\mathrm{V\ =\ LBH }$$ $$\hspace*{36 mm}\mathrm{=\ 65\ \times\ 40\ \times\ 24\ cm^3 }$$ $$\hspace*{36 mm}\mathrm{=\ 62\ 400\ cm^3 }$$

$$\hspace*{6 mm}\mathrm{4.3\kern2mmLength\ of\ cylinder\ =\ height\ =\ h }$$ $$\hspace*{40 mm}\mathrm{h\ =\ 450\ mm\ = \frac{450}{10}\ cm }$$ $$\hspace*{44 mm}\mathrm{=\ \frac{450}{10}\ cm }$$

$$\hspace*{44 mm}\mathrm{=\ 45\ cm \kern40mm }$$
$$\hspace*{13 mm}\mathrm{SA\ =\ \pi\times\ d\times(h\ +\ \frac12\times\ d)\ cm^2 }$$

$$\hspace*{13 mm}\mathrm{SA\ =\ \pi\times\ 6\times(45\ +\ \frac12\times6)\ cm^2 }$$ $$\hspace*{20 mm}\mathrm{=\ 904,779\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ of\ cylinder\ =\ V \kern30mm }$$

$$\hspace*{37 mm}\mathrm{V\ =\ \frac{\pi\times\ D^2\times\ h}{4} \kern30mm }$$

$$\hspace*{41 mm}\mathrm{=\ \frac{\pi\times\ 6^2\times\ 45}{4} }$$

$$\hspace*{41 mm}\mathrm{=\ 1\ 272,345\ cm^3 }$$

$$\hspace*{37 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Length\ of\ cylinder\ =\ height\ =\ h }$$ $$\hspace*{40 mm}\mathrm{h\ =\ 450\ mm\ = \frac{450}{10}\ cm }$$ $$\hspace*{44 mm}\mathrm{=\ \frac{450}{10}\ cm }$$

$$\hspace*{44 mm}\mathrm{=\ 45\ cm \kern40mm }$$
$$\hspace*{13 mm}\mathrm{Radius\ of\ cylinder\ =\ r\ =\ \frac12\ D }$$
$$\hspace*{51 mm}\mathrm{=\ 3\ cm }$$

$$\hspace*{13 mm}\mathrm{SA\ =\ 2\pi\ r(r\ +\ h) }$$

$$\hspace*{13 mm}\mathrm{SA\ =\ 2\times\ \pi\times\ 3\times(3\ +\ 45)\ cm^2 }$$ $$\hspace*{20 mm}\mathrm{=\ 904,779\ cm^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ of\ cylinder\ =\ V \kern30mm }$$

$$\hspace*{37 mm}\mathrm{V\ =\ \pi\ r^2\ h \kern30mm }$$
$$\hspace*{41 mm}\mathrm{=\ \pi\times\ 3^2\times 45\ cm^3 }$$
$$\hspace*{41 mm}\mathrm{=\ 1\ 272,345\ cm^3 }$$

Antwoorde / Answers  5

$$\hspace*{6 mm}\mathrm{5.1\kern2mmOppervlakte\ van\ bedding\ =\ LB }$$ $$\hspace*{52 mm}\mathrm{=\ 9\ \times 4\ m^2 \kern30mm }$$ $$\hspace*{52 mm}\mathrm{=\ 36\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.2\kern2mmOppervlakte\ van\ paadjie\ =\ }$$ $$\hspace*{21 mm}\mathrm{oppervlakte\ van\ 2\ lang\ dele\ + }$$ $$\hspace*{21 mm}\mathrm{oppervlakte\ van\ 2\ kort\ dele }$$ $$\hspace*{20 mm}\mathrm{=\ 2\times (11\times 1)\ +\ 2\times (4\times\ 1)\ m^2 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 22\ +\ 8\ m^2 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 30\ m^2 \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O \bold F }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ paadjie\ =\ totale\ oppv.\ ─\ }$$ $$\hspace*{39 mm}\mathrm{oppv.\ blombedding }$$ $$\hspace*{35 mm}\mathrm{=\ LB\ ─\ LB \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 11\ \times\ 6\ ─\ 9\ \times\ 4\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 66\ ─\ 36\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 30\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.3\kern2mmAantal\ stene }$$ $$\hspace*{18 mm}\mathrm{=\ oppervlakte\ van\ paadjie \times\ 50 }$$ $$\hspace*{18 mm}\mathrm{=\ 30\ \times\ 50 \kern30mm }$$ $$\hspace*{18 mm}\mathrm{=\ 1\ 500 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.4\kern2mmAantal\ pakke \kern40mm }$$ $$\hspace*{30 mm}\mathrm{=\ \frac{Aantal\ stene}{Aantal\ stene\ per\ pak} }$$

$$\hspace*{30 mm}\mathrm{=\ \frac{1\ 500}{500} }$$

$$\hspace*{30 mm}\mathrm{=\ 3 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Koste\ =\ R1\ 130\ \times\ 3 \kern30mm }$$ $$\hspace*{24 mm}\mathrm{=\ R3\ 390 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.1\kern2mmArea\ of\ flowerbed\ =\ LB }$$ $$\hspace*{43 mm}\mathrm{=\ 9\ \times 4\ m^2 \kern30mm }$$ $$\hspace*{43 mm}\mathrm{=\ 36\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.2\kern2mmArea\ of\ path\ =\ area\ of\ 2\ long\ parts }$$ $$\hspace*{35 mm}\mathrm{+\ area\ of\ 2\ short\ parts }$$ $$\hspace*{35 mm}\mathrm{=\ 2\times (11\times 1)\ + \kern30mm }$$ $$\hspace*{39 mm}\mathrm{2\times (4\times\ 1)\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 22\ +\ 8\ m^2 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 30\ m^2 \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O \bold R }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ path\ =\ total\ area\ ─\ }$$ $$\hspace*{39 mm}\mathrm{area\ of\ flower\ bed }$$ $$\hspace*{35 mm}\mathrm{=\ LB\ ─\ LB \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 11\ \times\ 6\ ─\ 9\ \times\ 4\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 66\ ─\ 36\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 30\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.3\kern2mmNumber\ of\ bricks }$$ $$\hspace*{36 mm}\mathrm{=\ area\ of\ path\ \times\ 50 }$$ $$\hspace*{36 mm}\mathrm{=\ 30\ \times\ 50 \kern30mm }$$ $$\hspace*{36 mm}\mathrm{=\ 1\ 500 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{5.4\kern2mmNumber\ of\ packs \kern40mm }$$ $$\hspace*{30 mm}\mathrm{=\ \frac{Number\ of\ bricks}{Number\ of\ bricks\ per\ pack} }$$

$$\hspace*{30 mm}\mathrm{=\ \frac{1\ 500}{500} }$$

$$\hspace*{30 mm}\mathrm{=\ 3 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Cost\ =\ R1\ 130\ \times\ 3 \kern30mm }$$ $$\hspace*{22 mm}\mathrm{=\ R3\ 390 \kern30mm }$$

Antwoorde / Answers  6

$$\hspace*{6 mm}\mathrm{6.1\kern2mmOppervlakte\ van\ paadjie\ =\ }$$ $$\hspace*{21 mm}\mathrm{oppervlakte\ van\ 2\ lang\ dele\ + }$$ $$\hspace*{21 mm}\mathrm{oppervlakte\ van\ 2\ kort\ dele }$$ $$\hspace*{20 mm}\mathrm{=\ 2\times (19\times 2)\ +\ 2\times (5\times\ 2)\ m^2 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 76\ +\ 20\ m^2 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 96\ m^2 \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O \bold F }$$
$$\hspace*{13 mm}\mathrm{Oppervlakte\ paadjie\ =\ totale\ oppv.\ ─\ }$$ $$\hspace*{39 mm}\mathrm{oppv.\ blombedding }$$ $$\hspace*{35 mm}\mathrm{=\ LB\ ─\ LB \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 19\ \times\ 9\ ─\ 15\ \times\ 5\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 171\ ─\ 75\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 96\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{6.2\kern2mmTotale\ volume\ =\ TV }$$

$$\hspace*{13 mm}\mathrm{V(A),\ V(B)\ en\ V(C)\ =\ volume }$$ $$\hspace*{46 mm}\mathrm{van\ elke\ deel }$$ $$\hspace*{13 mm}\mathrm{TV\ =\ V(A)\ +\ V(B)\ +\ V(C) }$$ $$\hspace*{20 mm}\mathrm{=\ LBH\ +\ \frac12(a+b)hH\ +\ LBH \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 5\times2\times5\ +\ \frac12(2+1)\times5\times3\ + \kern30mm }$$ $$\hspace*{24 mm}\mathrm{7\ \times\ 1\ \times\ 5 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$
$$\hspace*{13 mm}\mathrm{Volume\ van\ liggaam\ =\ }$$ $$\hspace*{21 mm}\mathrm{opperv.\ van\ liggaam\ \times\ hoogte }$$

$$\hspace*{13 mm}\mathrm{Gebruik\ die\ sy-aansig,\ Fig.\ B,\ se }$$ $$\hspace*{13 mm}\mathrm{oppervlakte\ as\ die\ basis\ en\ die }$$ $$\hspace*{13 mm}\mathrm{breedte\ van\ die\ bad\ as\ die\ hoogte. }$$

$$\hspace*{13 mm}\mathrm{Kom\ ons\ gebruik\ V\ =\ volume\ van }$$ $$\hspace*{13 mm}\mathrm{die\ bad,\ A\ =\ oppervlakte\ van }$$ $$\hspace*{13 mm}\mathrm{sy-aansig\ en \kern40mm }$$ $$\hspace*{13 mm}\mathrm{H\ =\ die\ breedte\ van\ die\ bad. }$$

$$\hspace*{13 mm}\mathrm{Gebruik\ V\ =\ AH\ as\ ons\ "formule" }$$
$$\hspace*{13 mm}\mathrm{Gebruik\ die\ formule }$$ $$\hspace*{13 mm}\mathrm{A\ =\ \frac12\ \times\ (a\ +\ b)\ \times\ h\ om\ die }$$ $$\hspace*{13 mm}\mathrm{oppervlakte\ van\ 'n\ trapesium, }$$ $$\hspace*{13 mm}\mathrm{met\ a\ en\ b\ die\ ewewydige\ sye\ van }$$ $$\hspace*{13 mm}\mathrm{die\ trapesium\ en\ h\ die\ loodregte }$$ $$\hspace*{13 mm}\mathrm{afstand\ tussen\ die\ ewewydige\ sye, }$$ $$\hspace*{13 mm}\mathrm{te\ bereken. \kern40mm }$$

$$\hspace*{13 mm}\mathrm{Die\ diagramme\ hieronder\ toon }$$ $$\hspace*{13 mm}\mathrm{verskillende\ maniere\ om\ die }$$ $$\hspace*{13 mm}\mathrm{oppervlakte\ van\ die\ sy-aansig }$$ $$\hspace*{13 mm}\mathrm{te\ bereken. \kern40mm }$$

$$\hspace*{13 mm}\mathrm{Gebruik\ die\ metode\ wat\ jy\ die }$$ $$\hspace*{13 mm}\mathrm{beste\ verstaan. \kern30mm }$$

$$\hspace*{13 mm}\mathrm{A(A),\ A(B)\ en\ A(C)\ stel\ die }$$ $$\hspace*{13 mm}\mathrm{oppervlaktes\ van\ figure \kern30mm }$$ $$\hspace*{13 mm}\mathrm{A,\ B\ en\ C\ voor. \kern40mm }$$

$$\hspace*{13 mm}\mathrm{A(bad)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{26 mm}\mathrm{=\ LB\ +\ \frac12\ BH\ +\ LB }$$ $$\hspace*{26 mm}\mathrm{=\ 2\ \times\ 5\ +\ \frac12\ \times\ 3\ \times\ 1 }$$ $$\hspace*{30 mm}\mathrm{+\ 10\ \times\ 1 \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 21,5\ m^2 \kern40mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 \kern20mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern20mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$

$$\hspace*{13 mm}\mathrm{A(bad)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{25 mm}\mathrm{=\ LB\ +\ \frac12(a+b)\ \times\ H\ +\ LB }$$ $$\hspace*{25 mm}\mathrm{=\ 2\ \times\ 5\ +\frac12(2+1)\times3\ + }$$ $$\hspace*{30 mm}\mathrm{7\ \times\ 1 \kern30mm }$$ $$\hspace*{25 mm}\mathrm{=\ 21,5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000 \ell }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ m^3 }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$

$$\hspace*{13 mm}\mathrm{A(bad)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{25 mm}\mathrm{=\ LB\ +\ LB\ +\ \frac12BH }$$ $$\hspace*{25 mm}\mathrm{=\ 15\ \times\ 1\ +\ 5\ \times\ 1\ + }$$ $$\hspace*{30 mm}\mathrm{\frac12\ \times\ 3\ \times\ 1 }$$ $$\hspace*{25 mm}\mathrm{=\ 21,5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell \kern30mm }$$ 0 $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold F }$$

$$\hspace*{13 mm}\mathrm{A(bad)\ =\ A(A)\ ─\ A(B) }$$ $$\hspace*{25 mm}\mathrm{=\ LB\ ─\ \frac12(a+b)H }$$ $$\hspace*{25 mm}\mathrm{=\ 15\ \times\ 2\ ─\ \frac12\times(7+10)\times1 }$$ $$\hspace*{25 mm}\mathrm{=\ 21,5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{6 mm}\mathrm{6.3\kern2mmVolume\ om\ swembad\ te\ vul\ = }$$ $$\hspace*{38 mm}\mathrm{TV\ ─\ "oop\ spasie" \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Bereken\ die\ volume\ van\ die \kern30mm }$$ $$\hspace*{13 mm}\mathrm{"oop\ spasie"\ deur\ die\ totale \kern30mm }$$ $$\hspace*{13 mm}\mathrm{oppervlakte\ van\ die\ bad\ met }$$ $$\hspace*{13 mm}\mathrm{100\ mm\ te\ vermenigvuldig. }$$ $$\hspace*{13 mm}\mathrm{V(oop\ spasie)\ =\ 15\times5\times\frac{100}{1\ 000}\ m^3 \kern30mm }$$ $$\hspace*{37 mm}\mathrm{=\ 7,5\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ water\ om\ die\ ba te\ vul \kern30mm }$$ $$\hspace*{30 mm}\mathrm{=\ TV\ ─\ V(oop\ spasie)\ \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume(water)\ =\ 107,5\ ─\ 7,5\ m^3 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ m^3 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ 000\ \ell \kern30mm }$$

$$\hspace*{6 mm}\mathrm{6.1\kern2mmArea\ of\ path\ =\ area\ of\ 2\ long\ parts }$$ $$\hspace*{35 mm}\mathrm{+\ area\ of\ 2\ short\ parts }$$ $$\hspace*{35 mm}\mathrm{=\ 2\times (19\times 2)\ + \kern30mm }$$ $$\hspace*{39 mm}\mathrm{2\times (5\times\ 2)\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 76\ + 20\ m^2 }$$ $$\hspace*{35 mm}\mathrm{=\ 96\ m^2 \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O \bold R }$$
$$\hspace*{13 mm}\mathrm{Area\ of\ path\ =\ total\ area\ ─\ }$$ $$\hspace*{39 mm}\mathrm{area\ of\ flower\ bed }$$ $$\hspace*{35 mm}\mathrm{=\ LB\ ─\ LB \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 19\ \times\ 9\ ─\ 15\ \times\ 5\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 171\ ─\ 75\ m^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 96\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{6.2\kern2mmTotal\ volume\ =\ TV }$$

$$\hspace*{13 mm}\mathrm{V(A),\ V(B)\ and\ V(C)\ =\ volume }$$ $$\hspace*{48 mm}\mathrm{of\ each\ part }$$ $$\hspace*{13 mm}\mathrm{TV\ =\ V(A)\ +\ V(B)\ +\ V(C) }$$ $$\hspace*{20 mm}\mathrm{=\ LBH\ +\ \frac12(a+b)hH\ +\ LBH \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 5\times2\times5\ +\ \frac12(2+1)\times5\times3\ + \kern30mm }$$ $$\hspace*{24 mm}\mathrm{7\ \times\ 1\ \times\ 5 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{20 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$
$$\hspace*{13 mm}\mathrm{Volume\ of\ body\ =\ area\ of\ body }$$ $$\hspace*{45 mm}\mathrm{\times\ height \kern40mm }$$

$$\hspace*{13 mm}\mathrm{Use\ the\ side\ view\ of\ the\ pool, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Fig.\ B, as\ the\ base\ and\ the }$$ $$\hspace*{13 mm}\mathrm{breadth\ of\ the\ pool\ as\ the\ height. }$$

$$\hspace*{13 mm}\mathrm{Let\ us\ use\ V\ =\ volume\ of\ the\ pool, }$$ $$\hspace*{13 mm}\mathrm{A\ =\ area\ of\ side\ view\ and }$$ $$\hspace*{13 mm}\mathrm{H\ =\ the\ breadth\ of\ the\ pool. }$$

$$\hspace*{13 mm}\mathrm{Let\ us\ use\ V\ =\ AH\ as\ our\ "formula" \kern40mm }$$
$$\hspace*{13 mm}\mathrm{Let\ us\ use\ the\ formula \kern30mm }$$ $$\hspace*{13 mm}\mathrm{A\ =\ \frac12\ \times\ (a\ +\ b)\ \times\ h\ to\ calculate }$$ $$\hspace*{13 mm}\mathrm{the\ area\ of\ a\ trapezium\ with\ a\ and\ b }$$ $$\hspace*{13 mm}\mathrm{the\ parallel\ sides\ and\ h\ the }$$ $$\hspace*{13 mm}\mathrm{perpendicular\ distance\ between }$$ $$\hspace*{13 mm}\mathrm{the\ parallel\ sides. }$$

$$\hspace*{13 mm}\mathrm{The\ diagrams\ below\ show\ different }$$ $$\hspace*{13 mm}\mathrm{ways\ to\ calculate\ the\ area\ of }$$ $$\hspace*{13 mm}\mathrm{the\ side\ view\ of\ the\ pool. }$$ $$\hspace*{13 mm}\mathrm{Use\ the\ method\ that\ you \kern40mm }$$ $$\hspace*{13 mm}\mathrm{understand\ best. \kern40mm }$$

$$\hspace*{13 mm}\mathrm{A(A),\ A(B)\ and\ A(C)\ represent\ the }$$ $$\hspace*{13 mm}\mathrm{areas\ of\ figures\ A,\ B\ and\ C. \kern40mm }$$

$$\hspace*{13 mm}\mathrm{A(pool)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{26 mm}\mathrm{=\ LB\ +\ \frac12\ BH\ +\ LB }$$ $$\hspace*{26 mm}\mathrm{=\ 2\ \times\ 5\ +\ \frac12\ \times\ 3\ \times\ 1 }$$ $$\hspace*{30 mm}\mathrm{+\ 10\ \times\ 1 \kern30mm }$$ $$\hspace*{30 mm}\mathrm{=\ 21,5\ m^2 \kern40mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 \kern20mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern20mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$

$$\hspace*{13 mm}\mathrm{A(pool)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{26 mm}\mathrm{=\ LB\ +\ \frac12(a+b)\ \times\ H\ +\ LB }$$ $$\hspace*{26 mm}\mathrm{=\ 2\ \times\ 5\ +\ \frac12(2+1)\ \times\ 3\ + }$$ $$\hspace*{32 mm}\mathrm{7\ \times\ 1 \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 21.5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 }$$ $$\hspace*{26 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 107,5\ \times\ 1\ 000 \ell \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 107\ 500\ \ell }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$

$$\hspace*{13 mm}\mathrm{A(pool)\ =\ A(A)\ +\ A(B)\ +\ A(C) }$$ $$\hspace*{26 mm}\mathrm{=\ LB\ +\ LB\ +\ \frac12BH }$$ $$\hspace*{26 mm}\mathrm{=\ 15\ \times\ 1\ +\ 5\ \times\ 1\ + }$$ $$\hspace*{32 mm}\mathrm{\frac12\ \times\ 3\ \times\ 1 \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 21.5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 }$$ $$\hspace*{26 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{26 mm}\mathrm{=\ 107,5\ \times\ 1\ 000 \ell \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{36 mm}\mathrm{\bold O\bold R }$$

$$\hspace*{13 mm}\mathrm{A(bad)\ =\ A(A)\ ─\ A(B) }$$ $$\hspace*{25 mm}\mathrm{=\ LB\ ─\ \frac12(a+b)H }$$ $$\hspace*{25 mm}\mathrm{=\ 15\ \times\ 2\ ─\ \frac12\times(7+10)\times1 }$$ $$\hspace*{25 mm}\mathrm{=\ 21,5\ m^2 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ =\ AH \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 21,5\ \times\ 5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ m^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107,5\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 107\ 500\ \ell \kern30mm }$$

$$\hspace*{6 mm}\mathrm{6.3\kern2mmVolume\ to\ fill\ the\ pool\ = \kern30mm }$$ $$\hspace*{13 mm}\mathrm{TV\ ─\ "open\ space" \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Calculate\ the\ volume\ of\ the \kern30mm }$$ $$\hspace*{13 mm}\mathrm{"unfilled\ space"\ by\ multiplying\ the \kern30mm }$$ $$\hspace*{13 mm}\mathrm{total\ area\ of\ the\ pool\ by\ 100\ mm }$$ $$\hspace*{13 mm}\mathrm{V(open\ space)\ =\ 15\times5\times\frac{100}{1\ 000}\ m^3 \kern30mm }$$ $$\hspace*{39 mm}\mathrm{=\ 7,5\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume\ water\ to\ fill\ the\ pool \kern30mm }$$ $$\hspace*{30 mm}\mathrm{=\ TV\ ─\ V)open\ space)\ \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Volume(water)\ =\ 107,5\ ─\ 7,5\ m^3 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ m^3 \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ \times\ 1\ 000\ \ell \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 100\ 000\ \ell \kern30mm }$$

Antwoorde / Answers  7

$$\hspace*{6 mm}\mathrm{7.1.1\kern2mmDeursnit\ =\ 7\ m \kern30mm }$$
$$\hspace*{6 mm}\mathrm{7.1.2\kern2mmBreedte\ =\ 5\ m }$$
$$\hspace*{6 mm}\mathrm{7.1.3\kern2mmLengte\ =\ 8\ m \kern30mm }$$
$$\hspace*{6 mm}\mathrm{7.1.4\kern2mmWydte\ =\ 1\ m }$$

$$\hspace*{6 mm}\mathrm{7.2\kern2mm \kern30mm }$$

$$\hspace*{13 mm}\mathrm{s^2\ =\ b^2\ +\ h^2\ \cdots Pythagoras \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 2,5^2\ +\ 2,5^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 12,5 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{s\ =\ \sqrt{12,5} \kern30mm }$$ $$\hspace*{17 mm}\mathrm{=\ 3,536 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Skuinssye\ =\ 3,536\ m }$$

$$\hspace*{6 mm}\mathrm{7.3\kern2mmTA\ =\ \frac{\pi\ D^2}{8}\ +\ LB\ +\ \frac12BH \kern30mm }$$

$$\hspace*{19 mm}\mathrm{=\ \frac{\pi\times7^2}{8}\ +\ 8\times 7\ + \kern30mm }$$

$$\hspace*{23 mm}\mathrm{\frac12 \times\ 7\ \times\ 3,5\ \kern30mm }$$

$$\hspace*{19 mm}\mathrm{=\ 19,242\ +\ 56\ +\ 12,25\ m^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 87,492\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{7.4\kern2mmOppervlakte\ van\ paadjie\ =\ \kern30mm }$$ $$\hspace*{19 mm}\mathrm{Totale\ oppervlakte(TA)\ ─ \kern30mm }$$ $$\hspace*{24 mm}\mathrm{oppervlakte\ van\ bedding \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Oppervlakte\ paadjie\ =\ \kern30mm }$$ $$\hspace*{19 mm}\mathrm{87,492\ ─\ \Big(\frac{\pi D^2}{8}\ +\ LB\ +\ \frac12BH \Big)\ m^2 \kern30mm }$$

$$\hspace*{19 mm}\mathrm{87,492\ ─ \kern30mm }$$
$$\hspace*{17 mm}\mathrm{\Big(\frac{\pi\times5^2}{8}+8\times5\ +\frac12\times5\times2,5 \Big)\ m^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 87,492\ ─\ [9,817+40+6,25] \kern30mm }$$
$$\hspace*{19 mm}\mathrm{=\ 87,492\ ─\ 56,067\ m^2 \kern30mm }$$
$$\hspace*{19 mm}\mathrm{=\ 31,425\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{7.1.1\kern2mmDiameter\ =\ 7\ m \kern30mm }$$
$$\hspace*{6 mm}\mathrm{7.1.2\kern2mmBreadth\ =\ 5\ m }$$
$$\hspace*{6 mm}\mathrm{7.1.3\kern2mmLength\ =\ 8\ m \kern30mm }$$
$$\hspace*{6 mm}\mathrm{7.1.4\kern2mmWidth\ =\ 1\ m }$$

$$\hspace*{6 mm}\mathrm{7.2\kern2mm \kern30mm }$$

$$\hspace*{13 mm}\mathrm{s^2\ =\ b^2\ +\ h^2\ \cdots Pythagoras \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 2,5^2\ +\ 2,5^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 12,5 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{s\ =\ \sqrt{12,5} \kern30mm }$$ $$\hspace*{17 mm}\mathrm{=\ 3,536 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Hypotenuse\ =\ 3,536\ m }$$

$$\hspace*{6 mm}\mathrm{7.3\kern2mmTA\ =\ \frac{\pi\ D^2}{8}\ +\ LB\ +\ \frac12BH \kern30mm }$$

$$\hspace*{19 mm}\mathrm{=\ \frac{\pi\times7^2}{8}\ +\ 8\times 7\ + \kern30mm }$$

$$\hspace*{23 mm}\mathrm{\frac12 \times\ 7\ \times\ 3,5\ \kern30mm }$$

$$\hspace*{19 mm}\mathrm{=\ 19,242\ +\ 56\ +\ 12,25\ m^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 87,492\ m^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{7.4\kern2mmArea\ of\ path\ =\ Total\ area(TA)\ ─ \kern30mm }$$ $$\hspace*{44 mm}\mathrm{area\ of\ bed \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Area\ of\ path\ =\ \kern30mm }$$ $$\hspace*{19 mm}\mathrm{87,492\ ─\ \Big(\frac{\pi D^2}{8}\ +\ LB\ +\ \frac12BH \Big)\ m^2 \kern30mm }$$

$$\hspace*{19 mm}\mathrm{87,492\ ─ \kern30mm }$$
$$\hspace*{17 mm}\mathrm{\Big(\frac{\pi\times5^2}{8}+8\times5\ +\frac12\times5\times2,5 \Big)\ m^2 \kern30mm }$$ $$\hspace*{19 mm}\mathrm{=\ 87,492\ ─\ [9,817+40+6,25] \kern30mm }$$
$$\hspace*{19 mm}\mathrm{=\ 87,492\ ─\ 56,067\ m^2 \kern30mm }$$
$$\hspace*{19 mm}\mathrm{=\ 31,425\ m^2 \kern30mm }$$

Antwoorde / Answers  8

$$\hspace*{6 mm}\mathrm{8.1\kern2mmOppervlakte\ =\ \frac{\pi\ D^2}{4}\ \kern30mm }$$

$$\hspace*{35 mm}\mathrm{=\ \frac{\pi\times(380\div10)^2}{4}\ cm^2 \kern30mm }$$ $$\hspace*{35 mm}\mathrm{=\ 1\ 134\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.2\kern2mmOppervlakte\ van\ vierkant\ =\ sy^2 \kern30mm }$$ $$\hspace*{43 mm}\mathrm{s^2\ =\ 1\ 134 \kern30mm }$$ $$\hspace*{43 mm}\mathrm{s\ =\ \sqrt{1\ 134}\ cm \kern30mm }$$ $$\hspace*{47 mm}\mathrm{=\ 33,675\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.3\kern2mmVolume\ =\ oppervlakte\ \times\ hoogte \kern30mm }$$ $$\hspace*{23 mm}\mathrm{V\ =\ 1\ 134\ \times\ (60\ \div\ 10)\ cm^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 6\ 804\ cm^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.4\kern2mmSement\ \bold: sand\ =\ 1\ \bold:\ 3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Totale\ volume\ =\ 50\ \times\ 6\ 804\ cm^3 \kern30mm }$$ $$\hspace*{37 mm}\mathrm{=\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Total\ \kern10mmVolume\ \kern8mmVolume \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ \kern6mmsement\ \kern10mmsand \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern4mm4\ \kern16mm1\ \kern18mm3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm340\ \kern10mm\frac14\times340\ \kern10mm\frac34\times340 \kern30mm }$$

$$\hspace*{10 mm}\mathrm{340\ 200\ \kern4mm\frac14\times340\ 200\ \kern3mm\frac34\times340\ 200 \kern30mm }$$

$$\hspace*{10 mm}\mathrm{340\ 200\ \kern8mm85\ 050\ \kern11mm255\ 150 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{\kern2mmVolume\ sement\ =\ 85\ 050\ cm^3\ en \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ sand\ =\ 255\ 150\ cm^3 \kern30mm }$$
$$\hspace*{38 mm}\mathrm{\bold O\bold F \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Volume\ sement\ =\ \frac14\ totale\ volume \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ \frac14\ \times\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ 85\ 050\ cm^3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Volume\ sand\ =\ \frac34\ totale\ volume \kern30mm }$$

$$\hspace*{35 mm}\mathrm{=\ \frac34\ \times\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{35 mm}\mathrm{=\ 255\ 150\ cm^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.1\kern2mmArea\ =\ \frac{\pi\ D^2}{4} \kern30mm }$$

$$\hspace*{25 mm}\mathrm{=\ \frac{\pi\times(380\div10)^2}{4}\ cm^2 \kern30mm }$$ $$\hspace*{25 mm}\mathrm{=\ 1\ 134\ cm^2 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.2\kern2mmArea\ of\ square\ =\ side^2\ =\ s^2 \kern30mm }$$ $$\hspace*{34 mm}\mathrm{s^2\ =\ 1\ 134 \kern30mm }$$ $$\hspace*{36 mm}\mathrm{s\ =\ \sqrt{1\ 134}\ cm \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ 33,675\ cm \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.3\kern2mmVolume\ =\ area\ \times\ height \kern30mm }$$ $$\hspace*{23 mm}\mathrm{V\ =\ 1\ 134\ \times\ (60\ \div\ 10)\ cm^3 \kern30mm }$$ $$\hspace*{27 mm}\mathrm{=\ 6\ 804\ cm^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{8.4\kern2mmCement\ \bold: sand\ =\ 1\ \bold:\ 3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Total\ volume\ =\ 50\ \times\ 6\ 804\ cm^3 \kern30mm }$$ $$\hspace*{33 mm}\mathrm{=\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Total\ \kern10mmVolume\ \kern8mmVolume \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ \kern6mmcement\ \kern10mmsand \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern4mm4\ \kern16mm1\ \kern18mm3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm340\ \kern10mm\frac14\times340\ \kern10mm\frac34\times340 \kern30mm }$$

$$\hspace*{10 mm}\mathrm{340\ 200\ \kern4mm\frac14\times340\ 200\ \kern3mm\frac34\times340\ 200 \kern30mm }$$

$$\hspace*{10 mm}\mathrm{340\ 200\ \kern8mm85\ 050\ \kern11mm255\ 150 \kern30mm }$$
$$\hspace*{13 mm}\mathrm{\kern2mmVolume\ of\ cement\ =\ 85\ 050\ cm^3\ and \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ of\ sand\ =\ 255\ 150\ cm^3 \kern30mm }$$
$$\hspace*{38 mm}\mathrm{\bold O\bold R \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Volume\ of\ cement\ =\ \frac14\ total\ volume \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ \frac14\ \times\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ 85\ 050\ cm^3 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{Volume\ of\ sand\ =\ \frac34\ of\ total\ volume \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ \frac34\ \times\ 340\ 200\ cm^3 \kern30mm }$$

$$\hspace*{40 mm}\mathrm{=\ 255\ 150\ cm^3 \kern30mm }$$

Antwoorde / Answers  9

$$\hspace*{6 mm}\mathrm{9.1\kern2mmVolume\ =\ oppervl.\ paadjie\ \times\ dikte \kern30mm }$$
$$\hspace*{35 mm}\mathrm{=\ 80\ \times\ \frac{150}{1\ 000}\ m^3 \kern30mm }$$

$$\hspace*{35 mm}\mathrm{=\ 12\ m^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.2\kern2mmVolume\ =\ oppervl.\ paadjie\ \times\ dikte \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Totale\ volume\ =\ TV, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ sement\ =\ Vc, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ sand\ =\ Vs\ en \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ klip\ =\ Vk \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern3mmTV \kern10mmVc \kern10mmVs\ \kern10mmVk \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern4mm7\ \kern12mm1\ \kern12mm2\ \kern12mm4 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern4mm1\ \kern11mm\frac17\ \kern11mm\frac27\ \kern11mm\frac47\ \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm12\ \kern6mm\frac17\times12\ \kern4mm\frac27\times12\ \kern5mm\frac47\times12 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm12\ \kern6mm1,714\ \kern5mm3,429\ \kern6mm6,857 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mmVolume\ van\ sement\ =\ 1,714\ m^3\ \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ van\ sand\ =\ 3,429\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ van\ klip\ =\ 6,857\ m^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.3\kern2mm25\ dm^3\ =\ \frac{25}{1\ 000}\ m^3 \kern30mm }$$
$$\hspace*{27 mm}\mathrm{=\ 0,025\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Aantal\ sakkies\ =\ \frac{1.714}{0,025} \kern30mm }$$ $$\hspace*{38 mm}\mathrm{=\ 68,56 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Dus\ 69\ sakkies\ sement\ is\ nodig. \kern30mm }$$

$$\hspace*{37 mm}\mathrm{\bold O\bold F \kern30mm }$$
$$\hspace*{13 mm}\mathrm{0,025\ m^3\ is\ die\ volume\ van\ 1\ sakkie \kern30mm }$$ $$\hspace*{13 mm}\mathrm{1\ m^3\ is\ die\ volume\ van\ \frac{1}{0,025}\ sakkies \kern30mm }$$ $$\hspace*{43 mm}\mathrm{i.e.\ 40\ sakkies \kern30mm }$$ $$\hspace*{13 mm}\mathrm{1,714\ m^3\ is\ die\ volume\ 1,714\times40\ sakkies \kern30mm }$$ $$\hspace*{40 mm}\mathrm{i.e.\ 68,56\ sakkies \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Dus\ 69\ sakkies\ sement\ is\ nodig. \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.4\kern2mmKoste\ van\ sement\ =\ R69\ \times\ 98,00 \kern30mm }$$ $$\hspace*{44 mm}\mathrm{=\ R6\ 762,00 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Koste\ van\ sand\ =\ R3,429\ \times\ 450,00 \kern30mm }$$
$$\hspace*{40 mm}\mathrm{=\ R1\ 543,05 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Koste\ van\ klip\ =\ R6,857\ \times\ 645,00 \kern30mm }$$
$$\hspace*{37 mm}\mathrm{=\ R4\ 422,77 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Totale\ koste\ =\ R12\ 727,82 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.1\kern2mmVolume\ =\ area\ of\ path\ \times\ thickness \kern30mm }$$
$$\hspace*{27 mm}\mathrm{=\ 80\ \times\ \frac{150}{1\ 000}\ m^3 \kern30mm }$$

$$\hspace*{27 mm}\mathrm{=\ 12\ m^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.2\kern2mmVolume\ =\ area\ of\ path\ \times\ thickness \kern30mm }$$
$$\hspace*{13 mm}\mathrm{Total\ volume\ =\ TV, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ of\ cement\ =\ Vc, \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ of\ sand\ =\ Vs\ and \kern30mm }$$ $$\hspace*{13 mm}\mathrm{volume\ of\ stone\ =\ Vk \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern3mmTV \kern10mmVc \kern10mmVs\ \kern10mmVk \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern4mm7\ \kern12mm1\ \kern12mm2\ \kern12mm4 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern4mm1\ \kern11mm\frac17\ \kern11mm\frac27\ \kern11mm\frac47\ \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm12\ \kern6mm\frac17\times12\ \kern4mm\frac27\times12\ \kern5mm\frac47\times12 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mm12\ \kern6mm1,714\ \kern5mm3,429\ \kern6mm6,857 \kern30mm }$$

$$\hspace*{13 mm}\mathrm{\kern2mmVolume\ of\ cement\ =\ 1,714\ m^3\ \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ of\ sand\ =\ 3,429\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{\kern2mmVolume\ of\ stone\ =\ 6,857\ m^3 \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.3\kern2mm25\ dm^3\ =\ \frac{25}{1\ 000}\ m^3 \kern30mm }$$
$$\hspace*{27 mm}\mathrm{=\ 0,025\ m^3 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Number\ of\ pockets\ =\ \frac{1.714}{0,025} \kern30mm }$$ $$\hspace*{45 mm}\mathrm{=\ 68,56 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Thus\ 69\ pockets\ of\ cement\ is\ needed. \kern30mm }$$
$$\hspace*{37 mm}\mathrm{\bold O\bold R \kern30mm }$$
$$\hspace*{13 mm}\mathrm{0,025\ m^3\ is\ the\ volume\ of\ 1\ pocket \kern30mm }$$ $$\hspace*{13 mm}\mathrm{1\ m^3\ is\ the\ volume\ of\ \frac{1}{0,025}\ pockets \kern30mm }$$ $$\hspace*{43 mm}\mathrm{i.e.\ 40\ pockets \kern30mm }$$ $$\hspace*{13 mm}\mathrm{1,714\ m^3\ is\ the\ volume\ 1,714\times40\ pockets \kern30mm }$$ $$\hspace*{40 mm}\mathrm{i.e.\ 68,56\ pockets \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Thus\ 69\ pockets\ of\ cement\ is\ needed. \kern30mm }$$

$$\hspace*{6 mm}\mathrm{9.4\kern2mmCost\ of\ cement\ =\ R69\ \times\ 98,00 \kern30mm }$$ $$\hspace*{40 mm}\mathrm{=\ R6\ 762,00 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Cost\ of\ sand\ =\ R3,429\ \times\ 450,00 \kern30mm }$$
$$\hspace*{35 mm}\mathrm{=\ R1\ 543,05 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Cost\ of\ stone\ =\ R6,857\ \times\ 645,00 \kern30mm }$$
$$\hspace*{36 mm}\mathrm{=\ R4\ 422,77 \kern30mm }$$ $$\hspace*{13 mm}\mathrm{Total\ cost\ =\ R12\ 727,82 \kern30mm }$$