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Year 11
Foundation

Surface area of composite solids

I can calculate the surface area of a composite solid.

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New
New
Year 11
Foundation

Surface area of composite solids

I can calculate the surface area of a composite solid.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The surface area of a composite solid is found by summing the area of all faces.
  2. The faces may not always be the same shape.
  3. The surface area may well be able to be calculated in a more efficient way.

Keywords

  • Surface area - 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.

  • Solid - A solid is a shape that has three dimensions (e.g. width, height and depth).

  • Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.

Common misconception

Pupils may not subtract overlapping faces from their surface area calculation.

Ask the pupils to visualise turning around/rotating the compound solid, and consider which faces of the component solids would always be hidden.

Encourage pupils to annotate diagrams to show how the are breaking down a compound/composite shape.
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.
A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the .
Correct Answer: apex, vertex
Q2.
This paper cup is cone-shaped. How many full paper cups of water can be poured into this cylindrical coffee mug?
An image in a quiz
2
2.5
Correct answer: 3
3.5
4
Q3.
The cone and cylinder share the same radius and vertical height. The volume of the cylinder is 1380 cm³. The volume of the cone is cm³.
An image in a quiz
Correct Answer: 460
Q4.
Which calculation gives the volume of this cone?
An image in a quiz
$$\frac{1}{3} \pi \times 16 \times 30$$
$$\frac{1}{3} \pi \times 16 \times 34 $$
Correct answer: $$\frac{1}{3} \pi \times 16^2 \times 30 $$
$$\frac{1}{3} \pi \times 8^2 \times 34$$
Q5.
The volume of this cone is cm³ to the nearest cubic centimetre.
An image in a quiz
Correct Answer: 8042
Q6.
The volume of this cone is 768𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is 𝜋 cm²
An image in a quiz
Correct Answer: 384

Exit quiz

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6 Questions

Q1.
A __________ shape is a shape created using two or more basic shapes.
Correct answer: composite
Correct answer: compound
dual
multiple
Q2.
This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.
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167 cm²
Correct answer: 334 cm²
344 cm²
354 cm²
Q3.
This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is cm².
An image in a quiz
Correct Answer: 528
Q4.
The composite solid is constructed by placing a hemisphere with diameter 10 cm on top of a cuboid. Find the surface area of the solid.
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391 cm²
Correct answer: 549 cm²
627 cm²
706 cm²
Q5.
The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 10 cm. Find the surface area of the solid.
An image in a quiz
534 cm²
Correct answer: 613 cm²
770 cm²
848 cm²
927 cm²
Q6.
The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is 𝜋 cm².
An image in a quiz
Correct Answer: 125