Volume of a frustum of a cone | Maths | Quizalize & Oak National Academy

Starter quiz

A ______ solid can be decomposed to make the volume easier to calculate.

'composite' ✓
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?

(4 × 16 + 8 × 4) × 6 ✓

4 × 6 × 16 + 12 × 6 × 4

4 × 16 × 6 + 8 × 6 × 4 ✓

16 × 12 × 6

2 × (12 × 4 × 6) ✓
This composite solid is constructed from two cuboids. All lengths given are in metres. The total volume of the solid is ______ m³.

'880' ✓
This composite solid is constructed by placing a hemisphere with diameter 10 cm on top of a cuboid. Find the volume of the solid. Give your answer to the nearest cubic centimetre.

652 cm³

862 cm³ ✓

1124 cm³

2694 cm³
This composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 12 cm. The volume of the solid is ______cm³ (correct to 4 significant figures).

'2149' ✓
This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is ______𝜋 cm³.

'264' ✓

Exit quiz

A ______ is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.

'frustum' ✓
The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.

a

⇔

15 cm ✓

b

⇔

5 cm ✓

c

⇔

20 cm ✓
The diagram shows a side elevation of a frustum. Find the volume of the large cone that the frustum is cut from. Give your answer correct to 3 significant figures.

3421 cm³ to 3 s.f.

9120 cm³ to 3 s.f.

12 500 cm³ to 3 s.f. ✓

50 200 cm³ to 3 s.f.
The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.

4294 cm³

7720 cm³ ✓

8790 cm³

12 500 cm³
A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 9 cm. The height of the small cone is ______ cm.

'30' ✓
A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 9 cm. The volume of the frustum is ______𝜋 cm

'2940' ✓

Worksheet

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Lesson Details

Key learning points

The frustum of a cone can be thought of as a cone with the top missing.
The volume of a frustum of a cone can be thought of as the difference between two cones' volumes.
This formula can be manipulated to rely on information from the frustum only.

Common misconception

Pupils may think that if you cut the height of the cone in a half, the resulting frustrum will have half the volume of the original cone.

The frustrum is actually seven eighths of the volume of the original cone; the small cone that was removed to create the frustrum is one eighth the volume of the original cone if the frustrum and the small cone have the same height.

Keywords

Frustum - A frustum is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.
Volume - Volume is the amount of space occupied by a closed 3D shape.