New
New
Year 11
Higher
Volume of a frustum of a cone
I can calculate the volume of a frustum of a cone.
New
New
Year 11
Higher
Volume of a frustum of a cone
I can calculate the volume of a frustum of a cone.
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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.
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.
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.
Links can be made to conversions between metric units of length, units of area or units of volume. This topic also provides opportunities to practice using Pythagoras' theorem or trigonometry in context.
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).
Lesson video
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Starter quiz
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6 Questions
Q1.
A solid can be decomposed to make the volume easier to calculate.
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?
4 × 6 × 16 + 12 × 6 × 4
16 × 12 × 6
Q3.
This composite solid is constructed from two cuboids. All lengths given are in metres. The total volume of the solid is m³.
Q4.
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
1124 cm³
2694 cm³
Q5.
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).
Q6.
This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is 𝜋 cm³.
Exit quiz
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6 Questions
Q1.
A is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.
Q2.
The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.
15 cm
5 cm
20 cm
Q3.
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.
50 200 cm³ to 3 s.f.
Q4.
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
8790 cm³
12 500 cm³
Q5.
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.
Q6.
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