The volume of a pyramid | Maths | Quizalize & Oak National Academy

Starter quiz

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

'pyramid' ✓
Which of these shapes are polyhedrons?

cuboid ✓

pentagon

prism ✓

pyramid ✓

sphere
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?

oblique square-based pyramid

oblique triangular-based pyramid

right square-based pyramid ✓

right triangular-based pyramid

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

$a$

⇔

80 cm ✓

$b$

⇔

58 cm ✓

$c$

⇔

70.5 cm (3 s.f.) ✓

not a marked length on the net

⇔

42 cm ✓
The diagram shows a pyramid and its net. The surface area of the pyramid is ______ cm². Do not round your answer.

'15680' ✓
The surface area of this pyramid is ______ cm².

'360' ✓

Exit quiz

Which of these 3D shapes are pyramids?

Shape a ✓

Shape b

Shape c

Shape d ✓

Shape e ✓
A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an ______.

'apex' ✓
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.

'36' ✓
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:

$\frac{1}{2}$

$\frac{1}{3}$ ✓

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{3}{4}$
The volume of a pyramid with a base of area 60 cm² and a perpendicular height of 12 cm is ______ cm²

'240' ✓
The volume of this square-based right pyramid is ______ cm³.

'200' ✓

Worksheet

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Lesson Details

Key learning points

There are many different types of pyramid.
The apex of the pyramid is not necessarily above the centre of the base.
The formula for the volume of a pyramid can be derived.

Common misconception

Pupils may use the edge length as the perpendicular height when calculating the volume.

Remind pupils that for any volume calculation, three perpendicular lengths are multiplied and in most pyramids the edge of a triangle is not perpendicular to the base. Also the edge of the triangles can be different in the pyramid.

Keywords

Pyramid - A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an apex.
Apex - The apex is the point (vertex) which is the greatest perpendicular distance from the base.
Right pyramid - When the apex lies directly above the centre of the base, then it is called a right pyramid.
Oblique pyramid - An oblique pyramid is when the apex is not directly above the centre of the base.