New
New
Year 11
Higher

Surface area of a frustum of a cone

I can calculate the surface area of a frustum of a cone.

New
New
Year 11
Higher

Surface area of a frustum of a cone

I can calculate the surface area of a frustum of a cone.

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Lesson details

Key learning points

  1. The frustum of a cone can be thought of as a cone with the top missing.
  2. Calculating the surface area for the frustum of a cone is a similar method to finding the area.
  3. There is an extra face to consider, the top of the frustum.

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.

  • Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

Common misconception

Pupils may confuse the slant length (which is needed to find the curved surface area of the cone or frustum) with the perpendicular (or vertical) height.

Encourage pupils to clearly label their diagrams, indicating the perpendicular height with a right-angle symbol. They may need to use Pythagoras' theorem or trigonometry to calculate the slant length.

Finding the surface area of a frustrum involves several multi-step calculations. Encourage pupils to label each calculation or use ratio tables to organise their working logically.
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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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.
Correct answer: frustum
hemi-cone
semi-cone
Q2.
The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.
An image in a quiz
Correct Answer:a,16 cm

16 cm

Correct Answer:b,4 cm

4 cm

Correct Answer:c,21 cm

21 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.
An image in a quiz
219 000 cm³
309 000 cm³
Correct answer: 803 000 cm³
3 210 000 cm³
Q4.
The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.
An image in a quiz
214 000 cm³
314 000 cm³
414 000 cm³
Correct answer: 494 000 cm³
1 110 000 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 12 cm. The height of the small cone is cm.
An image in a quiz
Correct Answer: 80
Q6.
The diagram shows a large cone with a frustum of height 20 cm and a small cone. The radius of the frustum base is 15 cm and the radius of its top is 12 cm. The volume of the frustum is 𝜋 cm³.
An image in a quiz
Correct Answer: 3660

6 Questions

Q1.
A circular cone has surfaces.
Correct Answer: 2, two
Q2.
The area of the curved surface of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 1080
Q3.
The total surface area of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 1692
Q4.
Work out the length of the side marked $$x$$ on this frustum.
An image in a quiz
8 cm
9 cm
Correct answer: 10 cm
11.31 cm
11.61 cm
Q5.
Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.
An image in a quiz
110𝜋 cm²
115𝜋 cm²
Correct answer: 120𝜋 cm²
125𝜋 cm²
Q6.
The total surface area of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 210