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.

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

The apex is the point (vertex) which is the greatest perpendicular distance from the base.

The surface area of a cone

Maths

In this unit, pupils have increased their knowledge of volume which is used in the compound measures unit as the formula for density involves volume. 

In the prior unit, pupils built upon their learning of the area of different shapes. In this unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

2D and 3D shape: surface area and volume (pyramids, spheres and cones)

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

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

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

The slant length of this cone is {{ }} cm. Give your answer correct to 2 decimal places.

The total surface area of this cone is {{ }} cm². Give your answer correct to 3 significant figures.

Match each measurement to the correct formula. 

Work out the volume of a sphere with radius 1.4 m. Give your answer correct to 2 decimal places.

A sphere has a radius of 9 mm. The volume of the sphere, in terms of 𝜋, is {{}}𝜋 mm³. 

$$ \frac{4}{3} \times \pi \times 6^3 \div 2$$

$$ \frac{1}{2} \times \frac{4}{3} \times \pi \times 6^3$$

$$ \frac{4}{3} \times \pi \times 3^3 \div 2$$

Which of these calculations finds the volume of a hemisphere with a radius of 6 cm?

The volume of a hemisphere with a radius of 6 cm, in terms of $$\pi$$, is {{ }}$$\pi$$ cm³. 

The volume of a hemisphere is 1152𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is {{ }}𝜋 cm².

Starter Quiz