New
New
Year 11
Higher

The volume of a cone

I can calculate the volume of a cone.

New
New
Year 11
Higher

The volume of a cone

I can calculate the volume of a cone.

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Lesson details

Key learning points

  1. The volume of a cone can be found by displacement.
  2. Putting a cone into a cylinder filled with water displaces the water.
  3. When the cone is removed, the water level drops.
  4. The volume of the cone is the difference between the volume of the cylinder and water.
  5. There is a formula you can use to calculate the volume of a cone.

Keywords

  • Cone - A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex/vertex.

  • Right cone - A line drawn through the apex and centre of the base of a right circular cone will be perpendicular to the base.

  • Volume - Volume is the amount of space occupied by a closed 3D shape.

Common misconception

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

Remind pupils that for any volume calculation, three perpendicular lengths are multiplied and the slant height is not perpendicular to the base in a right cone. They may need to use Pythagoras' theorem to find the perpendicular height.

Encourage pupils to clearly label on diagrams and in their solutions, if they have been given the radius or diameter of the circular base of the cone.
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 circular is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex or vertex.
Correct Answer: cone
Q2.
The curved surface of this cone is unfolded into a circular sector. Match each measurement to its value.
An image in a quiz
Correct Answer:The radius of the sector is…,8 cm

8 cm

Correct Answer:The arc length of the sector is…,6𝜋 cm

6𝜋 cm

Correct Answer:The area of the sector is…,24𝜋 cm²

24𝜋 cm²

Q3.
Calculate the area of the curved surface of this cone. Give your answer correct to 3 significant figures.
An image in a quiz
75.0 cm²
Correct answer: 118 cm²
137 cm²
255 cm²
Q4.
Calculate the total surface area of this cone. Give your answer correct to 3 significant figures.
An image in a quiz
Correct answer: 1130 cm²
817 cm²
754 cm²
314 cm²
Q5.
The slant length of this cone is cm.
An image in a quiz
Correct Answer: 17
Q6.
The total surface area, in term of $$\pi$$, of this cone is $$\pi$$ cm².
An image in a quiz
Correct Answer: 200

6 Questions

Q1.
A __________ is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex.
Correct answer: circular cone
circular prism
circular pyramid
sphere
Q2.
This paper cup is cone-shaped. It will take full paper cups of water to fill this cylindrical coffee mug.
An image in a quiz
Correct Answer: 3, three
Q3.
The cone and cylinder share the same radius and vertical height. The volume of the cylinder is 690 cm³. The volume of the cone is cm³.
An image in a quiz
Correct Answer: 230
Q4.
Which calculation gives the volume of this cone?
An image in a quiz
$$\frac{1}{3} \pi \times 8 \times 15 $$
$$\frac{1}{3} \pi \times 8 \times 17 $$
Correct answer: $$\frac{1}{3} \pi \times 8^2 \times 15 $$
$$\frac{1}{3} \pi \times 8^2 \times 17 $$
Q5.
The volume of this cone is cm³ to the nearest cubic centimetre.
An image in a quiz
Correct Answer: 1005
Q6.
The volume of this cone is 96𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is 𝜋 cm²
An image in a quiz
Correct Answer: 96