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

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.

A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.

Advanced problem solving with further surface area and volume

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)

Match each measurement to the correct formula.

The height of the juice will remain the same.

The diagram shows a cuboid juice carton which is partially filled with juice. Laura changes the orientation of the carton. Which statement is true?

The diagram shows a cuboid. The length of the base is 2 cm greater than the height. Find an expression for the volume of the cuboid.

The diagram shows a cuboid. The length of the base is 2 cm greater than the height. The volume of the cuboid is 90 cm³. The surface area of the cuboid is $$x$$ is {{ }} cm². 

The volume of the cone is 144𝜋 cm³. Its height is twice the length of its radius. The total surface area of the cone, in terms of 𝜋,  is {{ }}.

$$\frac{1}{3}\times \text{area of base} \times \text {height}$$ 

Select the algebraic expression for the volume of this cone. 

The volume of this cone is the same as the volume of a sphere with a radius of 12 cm. The height, $$x$$ of the cone is {{}} cm.

Find the surface area of a cube with a volume of 512 cm².

The height, $$h$$, of a cone is three times the length of its radius. Find an algebraic expression for the volume of the cone in terms of $$h$$.

The radius of a cylinder is half of the height of the cylinder. The volume of the cylinder is 1024𝜋 cm³. The surface area of the cylinder, in terms of 𝜋, is {{}} cm².

This lesson will be removed by end of Summer Term 2025.

Advanced problem solving with further surface area and volume

Lesson outcome

This lesson will be removed by end of Summer Term 2025.