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Form 2 Questions and Answers on Volume of Solids
The mass of 1
c
m
3
of lead is 11.4 g. Calculate the mass of a lead sphere whose radius is 15 cm.
(1m 34s)
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1.
Calculate the volume of a sphere whose radius is: (a) 4.8 cm (b) 21 cm
2.
A solid metal cylinder is 60 cm long and 18 cm in diameter. Determine the number of solid spheres of diameter 8 cm that can be moulded from the cylinder.
3.
The internal and external radii of a spherical shell are 8 cm and 9 cm respectively. Calculate the volume of the material of the shell to the nearest
c
m
3
.
4.
A cylindrical tank of radius 0.6 m contains water to a depth of 1 m. A solid metal sphere of radius 0.5 m is placed in it. Calculate the rise of the water level in centimetres.
5.
The volume of water in a measuring cylinder is 25. 2
c
m
3
. After a solid metal sphere is immersed into it, the measuring cylinder reads 29.4
c
m
3
. Calculate the radius of the sphere.
6.
The mass of 1
c
m
3
of lead is 11.4 g. Calculate the mass of a lead sphere whose radius is 15 cm.
7.
If 1
c
m
3
of copper metal has a mass of 8.88 g, calculate the mass of a quarter sphere of copper whose radius is 24 cm.
8.
A spherical container which is 30 cm in diameter is
3
4
full of water. The water is emptied into a cylindrical container of diameter 12 cm. Find the depth of the water in the cylindrical container.
9.
A solid copper sphere of diameter 36 cm is to be moulded from a copper wire 0.8 mm in diameter. Find the length of copper wire required to make the sphere?
10.
Find the volume of each of the following pyramids: (a) Triangular base, sides 5 cm, 12 cm and 13 cm, height 24 cm. (b) Square base, side 6 cm, height 10 cm. (c) Rectangular base, 8 cm by 10 cm, height 12 cm.
11.
Find the volume of each of the following right pyramids: (a) Rectangular base, 18 cm by 24 cm, slant edge 39 cm. (b) Square base, side 8 cm slant edge 8 cm. (c) Triangular base, sides 10 cm, 12 cm and 4 cm, height 24 cm.
12.
(a) The volume of a pyramid is 120
c
m
3
. Calculate its height and the surface area if the base is a square of side 6 cm. (b) Find the height of a pyramid with base area 24
c
m
2
and volume 96
c
m
3
.
13.
Calculate the height and the length of the slant edge of a right pyramid whose base is a square of side 5 cm and volume 125
c
m
3
.
14.
The volume of a right pyramid of height 16 cm on a square base is 192
c
m
3
. Calculate the length of the side of the base.
15.
VABCD is a right pyramid with a square base ABCD. Calculate its volume if the height is 12 cm and the slant edge is 16 cm.
16.
The figure below is a net of a pyramid with a square base of side 32 cm. The other four faces are isosceles triangles whose equal sides are 34 cm each. Calculate the volume of the pyramid.
17.
Calculate the volume of a pyramid of height 14 cm and a square base of side 24.
18.
A cone has a base radius of 9.44 cm and a volume of 113.6
c
m
3
. Calculate the height of the cone.
19.
Find the volume of the following cones: (a) Slant height 17 cm, height 7 cm. (b) Base radius 9 cm, height 24 cm.
20.
Find the volume of each of the following cones: (a) Base area 18
c
m
2
, height 6 cm. (b) Slant height 15 cm. height 9 cm. (c) Base perimeter 16 cm, height 10 cm.
21.
Calculate the total surface area and volume of a frustum of a pyramid whose ends are squares of 10 cm and 12 cm and the height between the two ends is 4 cm.
22.
A toy consists of a conical top and a cylindrical base. The diameter of the base is 5 cm and the height of the cylindrical part is 4 cm. If the total height of the toy is 9 cm, calculate: (a) its total surface area. (b) its total volume.
23.
A frustum is cut from a cone whose radius is r cm and height h cm. If the height of the frustum is t centimetres, express the volume of the frustum as a fraction of the volume of the cone.
24.
The figure below shows a triangle in which AB = 18 cm, BC = 6 cm, BD = 7 cm and DE is parallel to BC. If the triangle is rotated about AB, calculate: (a) the surface area of the cone formed. (b) the volume of the cone.
25.
A path is 300 m long and 1.8 m wide. Find the volume of gravel needed to cover it to a depth of 5 cm.
26.
Calculate the volume of a metal tube whose internal diameter is 70 mm and thickness 7 mm, if it is 15 cm long.
27.
A water tank of height 2.5 m has a uniform cross-section in the shape of a rectangle with semi-circular ends as shown in the figure below. The inside length of the tank is 7 m and its width 4 m. Calculate the: (a) area of the base. (b) volume of the tank. (c) capacity of the tank in litres.
28.
A steel metal bar has the shape of a regular hexagon of side 2 cm, and it is 20 cm long. Calculate: (a) the cross-section area of the metal bar. (b) the volume of the metal bar. (c) the mass in kilograms of the metal bar if 1
m
3
of steel weighs 7 800 kg.
29.
A concrete tower on which a water tank is to be placed has a uniform octagonal cross-section of side 3 m. If its height is 24 m, find the volume of concrete used to make it.
30.
A metal rod of 20 m length has an isosceles triangular base, where the equal side are 12 cm each. If the included angle in the base is 40°, calculate: (a) the area of the cross-section. (b) the volume of the metal rod. (c) the mass of the metal rod, if it is made of copper, whose density is 9 000 kg/
m
3
.
31.
The cross-section of a container is in the shape of a trapezium. The two parallel sides of the container are 3.6 m and 2.1 m long, while the perpendicular height between them is 2.4 m. If its length is 6 m, find the volume of the container.
32.
The figure below represents a swimming pool. Calculate: (a) the volume of the pool in cubic metres. (b) the capacity of the pool in litres.
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