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Lesson 10 of 16

Surface area of cuboids

I can appreciate the concept of surface area and find the surface area of cuboids.

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Lesson 10 of 16

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Surface area of cuboids

I can appreciate the concept of surface area and find the surface area of cuboids.

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Lesson details

Key learning points

The surface area of a 3D shape is the sum of the area of all the faces.
The net of a cuboid can help find the surface area.
The surface area of a cuboid can be found without drawing the net.

Keywords

Surface area - the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Net - The net of a 3D object is a 2D representation of its surfaces that can be folded up into the 3D object.

Common misconception

Any arrangement of 6 square-faces will result in the net of a cube.

Some arrangements of 6 squares will result in some of them overlapping when the shape is folded into 3D, resulting in an incomplete cube.

The practice task A has additional material that involves pupils cutting out potential nets of cubes and exploring which arrangements successfully become cubes. Where possible, bigger printing of the nets will make folding easier.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Select the correct value and units of measure that represent the area of this rectangle.

Correct answer: 144

Correct answer: cm²

Q2.
Which of these statements about this shape are correct?

This shape is a trapezium.

Correct answer: The perimeter of this shape is 100 cm.

The perimeter of this shape is 625 cm.

The area of this shape is 100 cm².

Correct answer: The area of this shape is 625 cm².

Q3.
The area of this rectangle is 40 cm². The value of $$m$$ is .

Correct Answer: 5, 5 cm, 5cm

Q4.
Starting with the smallest, put the value of each of the four missing lengths ($$a$$, $$b$$, $$c$$, $$d$$) in order of size.

1 - $$b$$

2 - $$c$$

3 - $$a$$

4 - $$d$$

Q5.
In this picture, the square on the left is congruent to each of the squares in the diagram on the right. The area of the diagram on the right is cm².

Correct Answer: 72, 72 cm², 72cm², 72 cm squared, 72cm squared

Q6.
In this picture, the rectangle on the left is congruent to each of the three rectangles in the diagram on the right. The area of one rectangle is cm².

Correct Answer: 72, 72 cm², 72cm², 72 cm squared, 72cm squared

Assessment exit quiz

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6 Questions

Q1.
Each of these compound shapes are different arrangements of six congruent squares. Which of the compound shapes are nets of a cube?

Correct answer: a

Correct answer: b

Correct answer: e

Q2.
Which of these compound shapes are nets of a cuboid?

Correct answer: b

Correct answer: d

Q3.
This diagram shows six rectangles that can be connected together to create the net of a cuboid. Match each rectangles to its area.

Correct Answer:a,40 cm²

40 cm²

Correct Answer:b,10 cm²

10 cm²

Correct Answer:c,16 cm²

16 cm²

Q4.
This is the net of a cuboid. The surface area of the cuboid after this net is folded up is cm².

Correct Answer: 58, 58 cm², 58cm², 58 cm squared, 58cm squared

Q5.
Some of the calculations to find the surface area of this cuboid are given. The value of $$b$$ is greater than the value of $$c$$. Match each missing length or area to its value.

Correct Answer:a,2 cm

2 cm

Correct Answer:b,11 cm

11 cm

Correct Answer:c,5 cm

5 cm

Correct Answer:d,174 cm²

174 cm²

Correct Answer:total area of visible faces,87 cm²

87 cm²

Q6.
A cuboid has been drawn on isometric paper, where each unit of isometric paper represents 1 inch. The total surface area of this cuboid is square inches.

Correct Answer: 90, 90 inches², 90inches², 90 square inches

Additional material

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Lesson appears in

UnitMaths / Perimeter, area and volume

Maths

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Surface area of cuboids

Surface area of cuboids

These resources will be removed by end of Summer Term 2025.

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Select the correct value and units of measure that represent the area of this rectangle.

Q2.Which of these statements about this shape are correct?

Q3.The area of this rectangle is 40 cm². The value of $$m$$ is .

Q4.Starting with the smallest, put the value of each of the four missing lengths ($$a$$, $$b$$, $$c$$, $$d$$) in order of size.

Q5.In this picture, the square on the left is congruent to each of the squares in the diagram on the right. The area of the diagram on the right is cm².

Q6.In this picture, the rectangle on the left is congruent to each of the three rectangles in the diagram on the right. The area of one rectangle is cm².

Assessment exit quiz

6 Questions

Q1.Each of these compound shapes are different arrangements of six congruent squares. Which of the compound shapes are nets of a cube?

Q2.Which of these compound shapes are nets of a cuboid?

Q3.This diagram shows six rectangles that can be connected together to create the net of a cuboid. Match each rectangles to its area.

Q4.This is the net of a cuboid. The surface area of the cuboid after this net is folded up is cm².

Q5.Some of the calculations to find the surface area of this cuboid are given. The value of $$b$$ is greater than the value of $$c$$. Match each missing length or area to its value.

Q6.A cuboid has been drawn on isometric paper, where each unit of isometric paper represents 1 inch. The total surface area of this cuboid is square inches.

Additional material

Lesson appears in

UnitMaths / Perimeter, area and volume

Maths

Q1.
Select the correct value and units of measure that represent the area of this rectangle.

Q2.
Which of these statements about this shape are correct?

Q3.
The area of this rectangle is 40 cm². The value of $$m$$ is .

Q4.
Starting with the smallest, put the value of each of the four missing lengths ($$a$$, $$b$$, $$c$$, $$d$$) in order of size.

Q5.
In this picture, the square on the left is congruent to each of the squares in the diagram on the right. The area of the diagram on the right is cm².

Q6.
In this picture, the rectangle on the left is congruent to each of the three rectangles in the diagram on the right. The area of one rectangle is cm².

Q1.
Each of these compound shapes are different arrangements of six congruent squares. Which of the compound shapes are nets of a cube?

Q2.
Which of these compound shapes are nets of a cuboid?

Q3.
This diagram shows six rectangles that can be connected together to create the net of a cuboid. Match each rectangles to its area.

Q4.
This is the net of a cuboid. The surface area of the cuboid after this net is folded up is cm².

Q5.
Some of the calculations to find the surface area of this cuboid are given. The value of $$b$$ is greater than the value of $$c$$. Match each missing length or area to its value.

Q6.
A cuboid has been drawn on isometric paper, where each unit of isometric paper represents 1 inch. The total surface area of this cuboid is square inches.