A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an apex.

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

When the apex lies directly above the centre of the base, then it is called a right pyramid.

An oblique pyramid is when the apex is not directly above the centre of the base.

The volume of a pyramid

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 pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an {{}}. 

A square-based pyramid has a volume of 324 cm³ and a perpendicular height of 12 cm. The perimeter of the square base is {{}} cm. 

A hexagonal prism has the same height as a hexagonal pyramid. The hexagons on both shapes are congruent. The pyramid is filled with sand and poured into the prism. The fraction of the prism filled is:

The volume of a pyramid with a base of area 60 cm² and a perpendicular height of 12 cm is {{ }} cm²

The volume of this square-based right pyramid is {{ }} cm³.

A {{}} is a 3D shape that has a polygonal base and triangular faces that meet at an apex.

Sam describes a 3D shape. Sam says, "My shape has an apex that is directly above the centre of its square base. All the faces other than the base are triangles." What is Sam's shape?

The diagram shows a pyramid and its net. Match each length marked on the net to the correct measurement on the pyramid.

The diagram shows a pyramid and its net. The surface area of the pyramid is {{ }} cm². Do not round your answer.

The surface area of this pyramid is {{ }} cm².

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

The volume of a pyramid

Lesson outcome

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