Junior Secondary · Mathematics

Areas and Volumes: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Areas and Volumes.

10 questions24 marksFree, no account

Question 1

1 mark

The radius of a right circular cone is 3 cm and its vertical height is 4 cm. Find the volume of the cone in terms of \(\pi\).

Question 2

1 mark

The heights of two similar cones are in the ratio \(2:3\). If the total surface area of the smaller cone is \(16\pi \text{ cm}^2\), find the total surface area of the larger cone in terms of \(\pi\).

Question 3

1 mark

A solid toy is formed by joining a right circular cone and a hemisphere. The cone has a base radius of \(3 \text{ cm}\) and a height of \(4 \text{ cm}\). The base of the cone is attached to the flat face of a hemisphere with the same radius. Calculate the total volume of the solid in terms of \(\pi\).

Question 4

1 mark

A solid right circular cylinder has a base radius of 4 cm and a height of 5 cm. Find its curved surface area in terms of \(\pi\).

Question 5

1 mark

Calculate the total surface area of a solid hemisphere with a radius of 6 cm in terms of \(\pi\).

Question 6

2 marks

Find the surface area of a sphere with a radius of \(7 \text{ cm}\) in terms of \(\pi\).

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

The heights of two similar pyramids are in the ratio \(3:4\). If the volume of the larger pyramid is \(128 \text{ cm}^3\), find the volume of the smaller pyramid.

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Question 8

6 marks

In the figure, a right prism of height \(20 \text{ cm}\) has a base sector \(OAB\) with a radius of \(10 \text{ cm}\) and \(\angle AOB = 90^\circ\). Calculate the total surface area of the prism in terms of \(\pi\).

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Question 9

3 marks

A right circular cone has a base radius of \(9 \text{ cm}\) and a slant height of \(15 \text{ cm}\).

(a) Find the vertical height of the cone.
(b) Calculate the volume of the cone in terms of \(\pi\).

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

In the figure, \(VABCD\) is a right pyramid with a square base \(ABCD\) of side length \(12 \text{ cm}\). The vertical height of the pyramid is \(8 \text{ cm}\).

(a) Find the volume of the pyramid.
(b) Find the length of the slant height of a triangular face.
(c) Find the total surface area of the pyramid.

Write your answer out first, then check it against the worked solution.

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