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.

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

The volume 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)

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. 

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

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.

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

$$\frac{1}{3} \pi \times 8^2 \times 17 $$

Which calculation gives the volume of this cone?

The volume of this cone is {{ }} cm³ to the nearest cubic centimetre.

The volume of this cone is 96𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is {{ }}𝜋 cm²

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. 

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.

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

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