# Form 2 Questions and Answers on Volume of Solids

In this session, Form 2 Questions on Volume of Solids will be covered.

Lessons (**32**) * SHARE*

- 1.
Calculate the volume of a sphere whose radius is:
(a) 4.8 cm
(b) 21 cm

1m 9s - 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.

1m 57s - 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 #cm^3#.

1m 20s - 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.

2m 6s - 5.
The volume of water in a measuring cylinder is 25. 2 #cm^3#. After a solid metal sphere is immersed into it, the measuring cylinder reads 29.4 #cm^3#. Calculate the radius of the sphere.

1m 59s - 6.
The mass of 1 #cm^3# of lead is 11.4 g. Calculate the mass of a lead sphere whose radius is 15 cm.

1m 34s - 7.
If 1 #cm^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.

1m 37s - 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.

1m 58s - 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?

2m 2s - 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.

3m 43s - 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.

8m 42s - 12.
(a) The volume of a pyramid is 120#cm^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 #cm^2# and volume 96#cm^3#.

4m 2s - 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#cm^3#.

3m 22s - 14.
The volume of a right pyramid of height 16 cm on a square base is 192 #cm^3#. Calculate the length of the side of the base.

1m 21s - 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.

3m 14s - 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.

3m 6s - 17.
Calculate the volume of a pyramid of height 14 cm and a square base of side 24.

0m 40s - 18.
A cone has a base radius of 9.44 cm and a volume of 113.6 #cm^3#. Calculate the height of the cone.

1m 15s - 19.
Find the volume of the following cones:
(a) Slant height 17 cm, height 7 cm.
(b) Base radius 9 cm, height 24 cm.

2m 37s - 20.
Find the volume of each of the following cones:
(a) Base area 18 #cm^2#, height 6 cm.
(b) Slant height 15 cm. height 9 cm.
(c) Base perimeter 16 cm, height 10 cm.

3m 11s - 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.

6m 10s - 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.

3m 43s - 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.

4m 46s - 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.

3m 11s - 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.

1m 19s - 26.
Calculate the volume of a metal tube whose internal diameter is 70 mm and thickness 7 mm, if it is 15 cm long.

3m 41s - 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.

3m 4s - 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.

6m 14s - 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.

4m 13s - 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#.

2m 39s - 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.

1m 45s - 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.

2m 18s

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