The volume of a cone | Maths | Quizalize & Oak National Academy

Starter quiz

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.

'cone' ✓
The curved surface of this cone is unfolded into a circular sector. Match each measurement to its value.

The radius of the sector is…

⇔

8 cm ✓

The arc length of the sector is…

⇔

6𝜋 cm ✓

The area of the sector is…

⇔

24𝜋 cm² ✓
Calculate the area of the curved surface of this cone. Give your answer correct to 3 significant figures.

75.0 cm²

118 cm² ✓

137 cm²

255 cm²
Calculate the total surface area of this cone. Give your answer correct to 3 significant figures.

1130 cm² ✓

817 cm²

754 cm²

314 cm²
The slant length of this cone is ______ cm.

'17' ✓
$The total surface area, in term of <Math>\pi</Math>, of this cone is <span class="blank">______</span> <Math>\pi</Math> cm².$

The total surface area, in term of $\pi$ , of this cone is ______ $\pi$ cm².

'200' ✓

Exit quiz

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.

circular cone ✓

circular prism

circular pyramid

sphere
This paper cup is cone-shaped. It will take ______ full paper cups of water to fill this cylindrical coffee mug.

'3' ✓
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.

'230' ✓
Which calculation gives the volume of this cone?

$\frac{1}{3} \pi \times 8 \times 15$

$\frac{1}{3} \pi \times 8 \times 17$

$\frac{1}{3} \pi \times 8^2 \times 15$ ✓

$\frac{1}{3} \pi \times 8^2 \times 17$
The volume of this cone is ______ cm³ to the nearest cubic centimetre.

'1005' ✓
The volume of this cone is 96𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is ______𝜋 cm²

'96' ✓

Worksheet

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Lesson Details

Key learning points

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

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.

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.