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Year 11
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The surface area of a pyramid

I can calculate the surface area of a pyramid.

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New
New
Year 11
Higher

The surface area of a pyramid

I can calculate the surface area of a pyramid.

Download all resources
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Share activities with pupils
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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. Although the base is a polygon, the sides are always triangles.
  4. The surface area of a pyramid is the sum of the area of all the faces.

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.

Common misconception

Pupils may think that a cone is a pyramid.

Remind pupils that a pyramid has a polygonal base, so a cone cannot be a pyramid as the base is a circle, which is not a polygon.

Further challenge questions can be derived where trigonometry is needed, to calculate the perpendicular height of the triangular faces.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
The net of a cylinder is made from two congruent circles and a .
Correct Answer: rectangle
Q2.
A cylindrical tube is cut and unfolded into a rectangle. Find the values of $$a$$ and $$b$$ on the lengths of the rectangle.
An image in a quiz
Correct answer: $$a=18$$
$$a=10$$
Correct answer: $$b=10 \pi$$
$$b=5 \pi $$
$$b=10 $$
Q3.
Which formula gives the surface area of the curved surface of a cylinder of radius $$r$$ and height $$h$$?
Correct answer: Surface area of curved surface = $$ 2\pi r h$$
Surface area of curved surface = $$ \pi r h$$
Surface area of curved surface = $$ \pi r^2 h$$
Surface area of curved surface = $$2 \pi r^2 + 2\pi r h$$
Surface area of curved surface = $$ 2\pi r^2 h$$
Q4.
Find the surface area of a cylinder with radius 6 cm and height 9 cm. Give your answer correct to 3 significant figures.
226 cm²
283 cm²
339 cm²
Correct answer: 565 cm²
1130 cm²
Q5.
A cylinder has a radius of 3 m and a height of 6 m. The surface area of the cylinder, in terms of $$\pi$$, is $$\pi$$m².
Correct Answer: 54
Q6.
The surface area of this cylinder is 120π cm². The length of marked $$x$$ is cm.
An image in a quiz
Correct Answer: 11

Exit quiz

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6 Questions

Q1.
Which of these 3D shapes is a pyramid?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q2.
Which of these shapes are polyhedrons?
cone
Correct answer: cube
cylinder
Correct answer: hexagonal prism
Correct answer: pyramid
Q3.
Jun describes a 3D shape. Jun says, "My shape has an apex that is directly above a vertex of its square base. All the faces other than the base are triangles." What is Jun's shape?
Correct answer: oblique square-based pyramid
oblique triangular-based pyramid
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:$$a$$,0.4 m

0.4 m

Correct Answer:$$b$$,0.29 m

0.29 m

Correct Answer:$$c$$,0.352 m (3 s.f.)

0.352 m (3 s.f.)

Correct Answer:not a marked length on the net ,0.21 m

0.21 m

Q5.
The diagram shows a pyramid and its net. The surface area of the pyramid is m². Do not round your answer.
An image in a quiz
Correct Answer: 0.392
Q6.
The surface area of this pyramid is cm².
An image in a quiz
Correct Answer: 1440