Volume of a cuboid Quiz (Grade 4)

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Volume of a cuboid — Notes & Worked Examples Show / Hide

Explanation:

The volume of a cuboid is the amount of 3D space inside it, measured in cubic units (cm³ or m³): Volume = length × width × height (V = l × w × h). For a cube of side s, Volume = s³.

Make sure all three dimensions are in the same unit before multiplying. For liquid capacity questions, remember the vital conversion: 1 litre = 1000 ml = 1000 cm³.

Example 1: A cuboid fish tank measures 50 cm by 30 cm by 40 cm. Work out its capacity in litres.

V = 50 × 30 × 40

= 60,000 cm³

÷ 1000 = 60 litres

Example 2: A cuboid has volume 180 cm³, length 9 cm, and width 4 cm. Find its height h.

9 × 4 × h = 180

36h = 180

h = 180 ÷ 36 = 5 cm

One Page Guide (PDF) Volume of a cuboid Worksheets

Question 1 IGCSE Nov 2021 2F Q9

[2 marks]

The diagram shows a cuboid.

Work out the volume of the cuboid.

cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
12 × 6 × 9 = 648 cm³ M1 A1

Answer: 648 cm³

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Question 2

[2 marks]

Here is a cuboid.

Work out the volume of the cuboid.

cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
8 × 4 × 5 = 160 cm³ M1 A1

Answer: 160 cm³

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Question 3 AQA Jun 2019 1F Q14

[2 marks]

Here is a cuboid.

Work out the volume.

Answer cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
Volume of cuboid = length × width × height M1
Volume = 7 × 5 × 10 = 350 cm³ A1

Answer: Answer 350 cm³

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Question 4 OCR Nov 2020 1F Q3

[2 marks]

Work out the volume of this cuboid.

cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
Volume = 7 × 2 × 5 = 70 cm³. M1 A1

Answer: 70 cm³

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Question 5 AQA Nov 2023 3F Q8

[2 marks]

Here is a cuboid.

Work out the volume of the cuboid.
Give your answer to 1 decimal place.

Answer cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
Volume = 6.75 × 3.8 × 2.7 = 69.255 cm³ M1
Rounded to 1 decimal place: 69.3 cm³. A1

Answer: Answer 69.3 cm³

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Question 6 AQA Nov 2019 3F Q22

[3 marks]

Here is a small cuboid and a cube.
Small cuboids and cubes are stacked in layers to make larger cuboids.
Here is a cuboid made with four layers.

Work out the total number of cubes used.

The pattern is continued to make a cuboid with volume 336 cm³
How many cubes are used?

Answer

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
Small cuboid has dimensions 6 cm × 2 cm × 2 cm, volume = 24 cm³ M1
Cube has dimensions 2 cm × 2 cm × 2 cm, volume = 8 cm³
Each layer has dimensions 6 cm × 4 cm × 2 cm, with volume 48 cm³ M1
Each layer contains 1 cuboid and 3 cubes (volume = 24 + 3 × 8 = 48 cm³)
Number of layers in a 336 cm³ cuboid = 336 ÷ 48 = 7 layers
Total cubes used = 7 × 3 = 21 cubes. A1

Answer: Answer 21

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Question 7

[4 marks]

A container is in the shape of a cuboid.

The container is 23 full of water.
A cup holds 275 ml of water.
What is the greatest number of cups that can be completely filled with water from the container?

Worked Solution & Answer

Volume of cuboid = 30 × 6 × 19 = 3420 cm³ M2
Water volume = 2/3 × 3420 = 2280 ml M1
Number of cups = 2280 ÷ 275 = 8.29... ⇒ 8 complete cups A1

Answer: 8

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Question 8 AQA Nov 2020 2H Q9

[4 marks]

Here is a cuboid.

(a) Assume that the total surface area of the cuboid is 200 cm²
Work out the volume of the cuboid. [3 marks]

Answer cm³

(b) In fact, the total surface area of the cuboid is smaller than 200 cm²
What does this mean about the volume of the cuboid?
Tick one box.
[ ] It is smaller than the answer to part (a)
[ ] It is bigger than the answer to part (a)
[ ] It is the same as the answer to part (a)
[ ] It could be any of the above [1 mark]

Worked Solution & Answer

(a)

(The volume of a cuboid is length × width × height)
Surface area = 2(5 × 5) + 4(5 × y) = 50 + 20y = 200. M1
20y = 150 ⇒ y = 7.5 cm. M1
Volume = 5 × 5 × 7.5 = 187.5 cm³. A1

Answer (a): Answer 187.5 cm³

(b)

(The volume of a cuboid is length × width × height)
Since the cross-sectional dimensions (5 cm by 5 cm) are fixed, a smaller surface area means a smaller length y, which gives a smaller volume. B1

Answer (b): It is smaller than the answer to part (a)

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Question 9

[5 marks]

The diagram shows a solid metal cuboid.
The areas of three of the faces are marked on the diagram.
The lengths, in cm, of the edges of the cuboid are whole numbers.

The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.
Work out the greatest number of these cubes that can be made.

Worked Solution & Answer

Edges are 9 cm, 5 cm and 3 cm (since 9×3=27, 9×5=45, 3×5=15) M2
Volume of cuboid = 9 × 5 × 3 = 135 cm³ M1
Volume of one cube = 2.5³ = 15.625 cm³ M1
Number of cubes = 135 ÷ 15.625 = 8.64 → 8 cubes. A1

Answer: 8

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Question 10 OCR Nov 2017 3F Q3

[5 marks]

(a) Calculate the volume of this cuboid. [2 marks]

cm³

(b) In this cuboid all lengths are in centimetres.
The cuboid has a volume of 320 cm³.
Find the value of k. [3 marks]

k =

Worked Solution & Answer

(a)

(The volume of a cuboid is length × width × height)
6 × 4 × 2 = 48 cm³. M1 A1

Answer (a): 48 cm³

(b)

(The volume of a cuboid is length × width × height)
5 × k × k = 320 M1
⇒ 5k² = 320 M1
⇒ k² = 64
⇒ k = 8. A1

Answer (b): k = 8

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Score: 0 / 10 (0 / 31 marks)

Volume of a cuboid Worksheets Next: Volume of a prism →

Grade 4 Quizzes

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction