WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
Buite-oppervlakte en volume van liggame.
GRAAD 10
NOG OEFENINGE
Buite-oppervlakte en volume van liggame.
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
Surface area and volume of regular bodies .
GRADE 10
MORE EXERCISES
Surface area and volume of regular bodies .
Jy mag die volgende formules
gebruik om onderstaande vrae
te beantwoord :
Gebruik die volgende afkortings
in die formules :
Lengte = l
Breedte = b
Hoogte = h
Basis = b
Middellyn = D / d
straal / radius = r
sy = s
Vertikale hoogte = H ;
Buite-oppervlakte = BO
Volume = V
Formules :
Reghoekige prisma
BO = 2(l + b)h + 2lb
V = lbh
Kubus
SA = 6s2
V = s3
Driehoekige prisma
BO = (s1 = s2 = s3)l + bh
V = ½bhl
Sfeer / Bal
BO = 4πr2
V = 4(⅓)πr3
Silinder
BO = 2πrh + 2π2
V = πr2h
Keël
BO = πr2 + πrl
V = ⅓πr2H
Piramiede
BO = 2sh + s2
V = ⅓s3H
Bereken die buite-oppervlakte
en volume van elke liggaam :
1.
[ A 1. ]
2.
[ A 2. ]
3.
[ A 3. ]
4.
[ A 4. ]
5.
[ A 5. ]
6.
[ A 6. ]
7.
[ A 7. ]
8.
[ A 8. ]
9.
[ A 9. ]
10.
[ A 10. ]
11.
[ A 11. ]
12.
[ A 12. ]
13.
[ A 13. ]
14.
[ A 14. ]
15. Ses lood sfere met radius
1,5 cm word gesmelt en dan
in 'n reghoekige vorm met
lengte 7 cm en breedte 4 cm
gegooi. Bereken die hoogte
van die lood in die vorm.
[ A 15. ]
16. 'n Silindriese tenk, middellyn
2 m, en hoogte = 3 m, word
gebruik om reënwater van
die dak af te stoor. Na 'n reën
bui is die tenk ¾ vol.
Bereken die volume van die
tenk in m3 en in liter,
as 1 dm3 = 1 000 ℓ
[ A 16. ]
17. 'n Reghoekige metaalplaat,
98 dm lank en 13 dm wyd,
word gerol om 'n oop
silinder te vorm.
17.1 Bereken die radius van
hierdie silinder.
[ A 17. ]
17.2 Die silinder kry nou 'n boom
maar nie 'n deksel nie.
Bereken die volume van die
water, in ℓ, wat hierdie
silinder kan bevat.
[ A 17. ]
18. 'n Piramiede het 'n vierkantige
basis met oppervlakte 16 m2.
Die vertikale hoogte is 3 m
en die skuinshoogte is 3,6 m.
Bereken die volume van die
piramiede.
[ A 18. ]
18. Willem wil 'n kegelvormige
wigwam bou. Die vloer het 'n
middellyn van 4 m, die
loodregte hoogte is 2,5 m
en die skuinshoogte is 3,2 m.
Bereken die lengte van die
seilmateriaal wat Willem moet
koop om die wigwam te bou.
Die materiaal is 4 m wyd.
[ A 19. ]
20. 'n Halwe sirkel, 'n vierkant met
sy lengte 1 m, en 'n reghoekige
driehoek word gesny uit 'n
reghoekige metaal plaat 5 m
lank en 2 m wyd.
Die diagram hieronder toon
die oorblywende stuk metaal.
Bereken die omtrek en die
oppervlakte van die
oorblywende plaat.
[ A 20. ]
You may use the following
formulae to answer the
questions below :
Use the following abbreviations
in the formulae :
Length = l
Breadth / Width = b
Height = h
Base = b
Diameter = D / d
Radius / radius = r
sy / side = s
Vertical height = H
Surface area = SA
Volume = V
Formulae :
Rectanglular prism
SA = 2(l + b)h + 2lb
V = lbh
Cube
SA = 6s2
V = s3
Trianglular prism
SA = (s1 = s2 = s3)l + bh
V = ½bhl
Sphere / Ball
SA = 4πr2
V = 4(⅓)πr3
Cylinder
SA = 2πrh + 2π2
V = πr2h
Cone
SA = πr2 + πrl
V = ⅓πr2H
Pyramid
SA = 2sh + s2
V = ⅓s3H
Calculate the surface area and
volume of every body :
1.
[ A 1. ]
2.
[ A 2. ]
3.
[ A 3. ]
4.
[ A 4. ]
5.
[ A 5. ]
6.
[ A 6. ]
7.
[ A 7. ]
8.
[ A 8. ]
9.
[ A 9. ]
10.
[ A 10. ]
11.
[ A 11. ]
12.
[ A 12. ]
13.
[ A 13. ]
14.
[ A 14. ]
15. Six lead spheres with a radius
of 1,5 cm are melted and the
molten lead is then cast into a
rectangular form with a
length 7 cm and breadth 4 cm.
Calculate the height of the lead
in the form.
[ A 15. ]
16. A cylindrical tank, diameter = 2 m,
and a height = 3 m, is used to
collect rainwater from a roof.
After one rain storm the tank is
¾ full. Calculate the volume of
the water in the tank in m3 and
in litres, if 1 dm3 = 1 000 ℓ
[ A 16. ]
17. A rectangular metal sheet,
98 dm long and 13 dm wide, is
rolled to form an open cylinder.
17.1 Calculate the radius of this
cylinder.
[ A 17. ]
17.2 The cylinder is now fitted with
a bottom but no lid.
Calculate the volume of water,
in ℓ, that this cylinder can
contain.
[ A 17. ]
18. A pyramid has a square base
with an area of 16 m2.
The perpendicular height of the
pyramid is 3 m and the slant
height is 3,6 m. Calculate the
volume of the pyramid.
[ A 18. ]
19. William wants to make a conical
shaped wigwam. The floor has a
diameter of 4 m, the vertical
height is 2,5 m and the slant
height is 3,2 m. Calculate the
length of the canvas that William
has to buy to make the wigwam.
The width of the canvas is 4 m.
[ A 19. ]
20. A semi-circle, a square,
side length 1 m, and a
rectangular triangle are cut from a
rectangualar metal sheet 5 m
long by 2 m wide.
The figure below shows the part
that is left over,
Calculate the perimeter and the
area of the left over metal.
[ A 20. ]