New
New
Year 11
Higher

Checking and securing understanding of surface area of cuboids

I can efficiently calculate the surface area of cubes and cuboids.

New
New
Year 11
Higher

Checking and securing understanding of surface area of cuboids

I can efficiently calculate the surface area of cubes and cuboids.

Lesson details

Key learning points

  1. The surface area of a solid is the sum of the area of all the faces.
  2. The net of a cuboid can help find the surface area.
  3. 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.

Several different nets of cuboids are included in the examples. If a pupil is not convinced that the given net will fold into a cuboid, get them to check that there are three pairs of congruent rectangles, and suggest that they highlight or label edges that will join up when the net is folded.
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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6 Questions

Q1.
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.
Correct answer: polyhedron
polygonal
pyramid
Q2.
Which of these 3D solids is a prism?
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
Q3.
A set of cuboids each have a volume of 240 cm³. Match each base of a cuboid to the correct height.
Correct Answer:Base: 4 cm by 6 cm,Height: 10 cm

Height: 10 cm

Correct Answer:Base: 5 cm by 4 cm,Height: 12 cm

Height: 12 cm

Correct Answer:Base: 15 cm by 4 cm,Height: 4 cm

Height: 4 cm

Correct Answer:Base: 8 cm by 6 cm,Height: 5 cm

Height: 5 cm

Correct Answer:Base: 10 cm by 4 cm,Height: 6 cm

Height: 6 cm

Q4.
The volume of this prism is cm³.
An image in a quiz
Correct Answer: 120
Q5.
The volume of this triangular prism is cm³.
An image in a quiz
Correct Answer: 720
Q6.
The volume of this prism is 280 cm³. The height of the prism is cm.
An image in a quiz
Correct Answer: 5.6

6 Questions

Q1.
The surface area is the __________ area of all the surfaces of a closed 3D shape.
product
quotient
Correct answer: total
Q2.
Here is a net of a cube. Which calculations correctly give the surface area of the cube?
An image in a quiz
7 + 7 + 7 + 7 + 7 + 7
Correct answer: 49 × 6
6 × 7
Correct answer: (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7)
Correct answer: (7 × 7) × 6
Q3.
Here is a net of a cuboid. What is the surface area of the cuboid?
An image in a quiz
24 cm²
48 cm²
176 cm²
Correct answer: 352 cm²
384 cm²
Q4.
The diagram shows the plan view and front and side elevations of a cuboid. The surface area of the cuboid is m².
An image in a quiz
Correct Answer: 78
Q5.
The diagram shows an isometric drawing of a cuboid. The surface area of the cuboid is m².
An image in a quiz
Correct Answer: 496
Q6.
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