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Year 11
Higher

The volume of a pyramid

I can calculate the volume of a pyramid.

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New
New
Year 11
Higher

The volume of a pyramid

I can calculate the volume of a pyramid.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. There are many different types of pyramid.
  2. The apex of the pyramid is not necessarily above the centre of the base.
  3. 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.

For challenge, questions can be created which links surface area of a pyramid and volume of a pyramid.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
A is a 3D shape that has a polygonal base and triangular faces that meet at an apex.
Correct Answer: pyramid
Q2.
Which of these shapes are polyhedrons?
Correct answer: cuboid
pentagon
Correct answer: prism
Correct answer: pyramid
sphere
Q3.
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
Correct answer: right square-based pyramid
right triangular-based pyramid
triangular prism
Q4.
The diagram shows a pyramid and its net. Match each length marked on the net to the correct measurement on the pyramid.
An image in a quiz
Correct Answer:$$a$$,80 cm

80 cm

Correct Answer:$$b$$,58 cm

58 cm

Correct Answer:$$c$$,70.5 cm (3 s.f.)

70.5 cm (3 s.f.)

Correct Answer:not a marked length on the net,42 cm

42 cm

Q5.
The diagram shows a pyramid and its net. The surface area of the pyramid is cm². Do not round your answer.
An image in a quiz
Correct Answer: 15680, 15,680, 15 680
Q6.
The surface area of this pyramid is cm².
An image in a quiz
Correct Answer: 360

Exit quiz

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6 Questions

Q1.
Which of these 3D shapes are pyramids?
An image in a quiz
Correct answer: Shape a
Shape b
Shape c
Correct answer: Shape d
Correct answer: Shape e
Q2.
A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an .
Correct Answer: apex
Q3.
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.
Correct Answer: 36
Q4.
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:
$$\frac{1}{2}$$
Correct answer: $$\frac{1}{3}$$
$$\frac{1}{4}$$
$$\frac{2}{3}$$
$$\frac{3}{4}$$
Q5.
The volume of a pyramid with a base of area 60 cm² and a perpendicular height of 12 cm is cm²
Correct Answer: 240
Q6.
The volume of this square-based right pyramid is cm³.
An image in a quiz
Correct Answer: 200