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 om onderstaande vrae
te beantwoord :
You may use the following formulae to
answer to questions below :
answer to questions below :
Gebruik die volgende afkortings : Use the following abbreviations :
Lengte / Length = l ; Breedte / Breadth / Width = b
; Hoogte / Height = h basis / base = b ;
Middellyn / Diameter = d ; straal / radius / radius = r
sy / side = s ; Vertikale hoogte / Vertical height = H ;
Liggaam / Body Buite-oppervlakte ( BO ) / Volume
Surface area ( SA )
Reghoekige prisma / BO / SA = 2(l + b)h + 2lb V = lbh
Rectanglular prism
Kubus / Cube BO / SA = 6s2 V = s3
Driehoekige prisma / BO / SA = (s1 + s2 + s3)l + bh V = ½bhl
Trianglular prism
4
Sfeer/bal/ Sphere/ball BO / SA = 4 π r2 V = ── πr3
3
Silinder / Cylinder BO / SA = 2πrh + 2πr2 V = πr3h
Keël / Cone BO / SA = 4 π r2 + π rl V = ⅓ πr2H
Piramiede / Pyramid BO / SA = 2sh + s2 V = ⅓ s3H
Bereken die buite-oppervlakte en volume van elke liggaam :
Calculate the surface area and volume of every body :
[ A 1. ] [ A 2. ] [ A 3. ]
[ A 4. ] [ A 5. ] [ A 6. ]
[ A 7. ] [ A 8. ] [ A 9. ]
[ A 10. ] [ A 11. ] [ A 12. ]
[ A 13. ] [ 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, vang reënwater op.
Na 'n bui is die tenk ¾ vol.
Bereken die volume van die water
in die tenk in m3 en in liter
as 1 m3 = 1 000 ℓ
[ A 16. ]
17. 'n Reghoekige metaalplaat, 98 dm
lank en 13 dm breed, word gerol
om 'n oop silinder te vorm.
17.1 Bereken die radius van die silinder.
[ A 17.1 ]
17.2 Die silinder word nou van 'n
boom maar nie 'n deksel voorsien.
Bereken die volume water, in ℓ,
wat die silinder kan bevat.
[ A 17.2 ]
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. ]
19. 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. ]
15. Six lead spheres with a radius
of 1,5 cm are melted and the
molted lead is then cast into a
rectangular form with 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 height = 3 m, is used to collect
rainwater from a roof. After one rainstorm
the tank is ¾ full.
Calculate the volume of the water in
the tank in m3 and in litres if 1 m3 = 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 17.1 ]
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 17.2 ]
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. ]