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.

Forming equations involving complex shape calculations

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.

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 9 cm. The height, $$x$$ of the cone is {{}} cm.

Find the volume of a cube with a surface area of 294 cm².

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

The radius of a cylinder is half of the height of the cylinder. The volume of the cylinder is 250𝜋 cm³. The surface area of the cylinder, in terms of 𝜋, is {{}} cm².

A 3D shape that has 2 surfaces is a __________.

The area of the curved surface of this frustum is {{ }}𝜋 cm². Leave your answer in terms of 𝜋.

The total surface area of this frustum is {{ }}𝜋 cm². Leave your answer in terms of 𝜋.

Work out the length of the side marked $$x$$ on this frustum.

Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.

This lesson will soon be taken down.

Forming equations involving complex shape calculations

Lesson outcome