Unit 22 Section 3 : Volume of a Cuboid

In this section, we consider the volume of any cuboid.

The volume of a cuboid
Volume of a cuboid = a × b × c = a b c
where a, b and c are the lengths of the sides of the cuboid.

Example
We want to find the volume of this cuboid in cm³.

To find the volume, we calculate 3 cm × 4 cm × 7 cm.
The volume of the cube is 84 cm³ (84 cubic centimetres).

Practice Question
Work out the answer to this question then click Click on this button below to see the correct answer to see whether you are correct.
A letter 'T' shape is made by sticking together 2 cuboids as shown in the diagram.
What is the total volume in cm³ of the letter 'T'?

 

Exercises

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Question 1
Calculate the volume of each of the cuboids below.

(a) cm³
(b) cm³
(c) m³
(d) m³

Question 2
A cuboid has sides of length 5 m, 3 m and 1 m.

(a) What is the volume of the cuboid in m³?
m³

(b) What is the volume of the cuboid in cm³?
cm³

Question 3
The diagram shows a large box and a small box, both of which are cuboids.

 

(a) Calculate the volume of the large box.
cm³

(b) Calculate the volume of the small box.
cm³

(c) How many of the small boxes would fit in the large box?

Question 4
A set of wooden building blocks contains wooden blocks that are 10 cm by 2 cm by 4 cm.
The blocks are used to make the shapes below. Calculate the volume of each shape.

(a) cm³
(b) cm³

Question 5
Calculate the volume of this cuboid, giving your answer:

(a) in m³, using decimals
m³

(b) in cm³
cm³

Question 6
A letter 'L' shape is made from 2 cuboids, marked A and B in the diagram below.

(a) Calculate the volume of cuboid A.
cm³

(b) Calculate the volume of cuboid B.
cm³

(c) Calculate the total volume of the letter 'L' shape.

Question 7
Calculate the volume of the solid below.
 

cm³

Question 8
The diagram shows a wooden block that has had a square hole cut through it.
 
Calculate the volume of wood in the block.
cm³

Question 9
The shape in the diagram below can be folded to form a cuboid.
 
Calculate the volume of the cuboid.
cm³

You have now completed Unit 22 Section 3
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Produced by A.J.Reynolds January 2001