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 solid is a shape that has three dimensions (e.g. width, height and depth).

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

Surface area of composite solids

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 __________ shape is a shape created using two or more basic shapes.

This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.

This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is {{ }} cm².

 The composite solid is constructed by placing a hemisphere with diameter 10 cm on top of a cuboid. Find the surface area of the solid. 

The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 10 cm.  Find the surface area of the solid. 

The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is {{ }}𝜋 cm².

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 {{}}. 

This paper cup is cone-shaped. How many full paper cups of water can be poured into this cylindrical coffee mug?

The cone and cylinder share the same radius and vertical height. The volume of the cylinder is 1380 cm³. The volume of the cone is {{ }} cm³.

$$\frac{1}{3} \pi \times 16^2 \times 30 $$

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 768𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is {{ }}𝜋 cm²

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

Surface area of composite solids

Lesson outcome

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