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Year 11

Higher

Volume of composite solids

I can calculate the volume of a composite solid.

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New

Year 11

Higher

Volume of composite solids

I can calculate the volume of a composite solid.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

A composite solid can be decomposed to make the volume easier to calculate.
Completing the solid may be a more useful method.
Decomposing and rearranging parts of the solid may be beneficial.

Keywords

Volume - The volume is the amount of space occupied by a closed 3D shape.
Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.

Common misconception

Pupils may only using given measures in their calculations, even when these are not the lengths required for substitution into a volume formula.

Encourage pupils to annotate diagrams to show how the are breaking down a compound/composite shape. Pupils should label the diagram with any new lengths needed. They may need to use Pythagoras or trigonometry to find these new lengths.

If some of the measurements are given in different units of length (such as cm and m), encourage the pupils to convert the lengths to the same unit, before starting the volume calculation.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

A shape created using two or more basic shapes is called a shape.

Correct Answer: composite, compound

Q2.

This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.

456 cm²

912 cm²

Correct answer: 952 cm²

982 cm²

Q3.

This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is cm².

Correct Answer: 168

Q4.

The composite solid is constructed by placing a hemisphere with diameter 8 cm on top of a cuboid. Find the surface area of the solid.

206 cm²

Correct answer: 306 cm²

357 cm²

407 cm²

Q5.

The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 12 cm. Find the surface area of the solid.

792 cm²

829 cm²

867cm²

Correct answer: 905 cm²

1018 cm²

Q6.

The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is 𝜋 cm².

Correct Answer: 72

Exit quiz

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6 Questions

Q1.

The amount of space occupied by a closed 3D shape is called the of the shape.

Correct Answer: volume

Q2.

The diagram shows a composite solid constructed from two congruent cuboids. All lengths given are in centimetres. Which of these calculations give the total volume of the solid?

Correct answer: 4 × 8 × 2 + 4 × 2 × 4

Correct answer: (2 × 6 + 6 × 2) × 4

4 × 2 × 8 + 2 × 4 × 8

6 × 4 × 8

Correct answer: 2 × 6 × 4 × 2

Q3.

This composite solid is constructed from two cuboids. All lengths given are in metres. The total volume of the solid is m³.

Correct Answer: 360

Q4.

This composite solid is constructed by placing a hemisphere with diameter 12 cm on top of a cuboid. Find the volume of the solid. Give your answer to the nearest cubic centimetre.

631 cm³

Correct answer: 932 cm³

1385 cm³

4099 cm³

Q5.

This composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 8 cm. The volume of the solid is cm³ (correct to 3 significant figures).

Correct Answer: 737

Q6.

This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is 𝜋 cm³.

Correct Answer: 891