Checking and securing understanding of surface area of cuboids | Maths

Starter quiz

A prism is a __________ with a base that is a polygon and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.

polyhedron ✓

polygonal

pyramid
Which of these 3D solids is a prism?
A set of cuboids each have a volume of 240 cm³. Match each base of a cuboid to the correct height.

Base: 4 cm by 6 cm

⇔

Height: 10 cm ✓

Base: 5 cm by 4 cm

⇔

Height: 12 cm ✓

Base: 15 cm by 4 cm

⇔

Height: 4 cm ✓

Base: 8 cm by 6 cm

⇔

Height: 5 cm ✓

Base: 10 cm by 4 cm

⇔

Height: 6 cm ✓
The volume of this prism is ______ cm³.

'120' ✓
The volume of this triangular prism is ______ cm³.

'720' ✓
The volume of this prism is 280 cm³. The height of the prism is ______ cm.

'5.6' ✓

Exit quiz

The surface area is the __________ area of all the surfaces of a closed 3D shape.

product

quotient

total ✓
Here is a net of a cube. Which calculations correctly give the surface area of the cube?

7 + 7 + 7 + 7 + 7 + 7

49 × 6 ✓

6 × 7

(7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) ✓

(7 × 7) × 6 ✓
Here is a net of a cuboid. What is the surface area of the cuboid?

24 cm²

48 cm²

176 cm²

352 cm² ✓

384 cm²
The diagram shows the plan view and front and side elevations of a cuboid. The surface area of the cuboid is ______m².

'78' ✓
The diagram shows an isometric drawing of a cuboid. The surface area of the cuboid is ______ m².

'496' ✓
Starting with the cuboid with the smallest surface area, put these cuboids in order of surface area size.

1

⇔

Purple cuboid: width 1 cm, height 4 cm and length 8 cm

2

⇔

Blue cuboid: width 2 cm, height 5 cm and length 5 cm

3

⇔

Red cuboid: width 3 cm, height 4 cm and length 5 cm

4

⇔

Yellow cuboid: width 4 cm, height 4 cm and length 4 cm

Worksheet

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Lesson Details

Key learning points

The surface area of a solid 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.

Common misconception

When working out the surface area, the pupil may only find the sum of the areas of three faces of a cuboid (for example the visible sides in a 3D drawing), instead of all six faces.

Encourage pupils to sketch the net of the cuboid as part of their solution. This will provide a visual reminder to the pupil to find the area of all six faces, as well as making it easier to check their answer.

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.
Net - The net of a 3D object is a 2D representation of its surfaces that can be folded up into the 3D object.