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      Surface area of cuboids

      Lesson details

      Learning outcome

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

      Key learning points

      1. The surface area of a 3D shape 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.

      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.

      Teacher tip

      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.

      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).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

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

      An image in a quiz
      25
      50
      Correct answer: 144
      cm
      Correct answer: cm²

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

      An image in a quiz
      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 .

      An image in a quiz
      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.

      An image in a quiz
      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.

      An image in a quiz
      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.

      An image in a quiz
      Correct Answer: 72, 72 cm², 72cm², 72 cm squared, 72cm squared

      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?

      An image in a quiz
      Correct answer: a
      Correct answer: b
      c
      d
      Correct answer: e

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

      An image in a quiz
      a
      Correct answer: b
      c
      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.

      An image in a quiz
      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.

      An image in a quiz
      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.

      An image in a quiz
      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.

      An image in a quiz
      Correct Answer: 90, 90 inches², 90inches², 90 square inches

      To help you plan your 8 maths lesson on: Surface area of cuboids, download all teaching resources for free and adapt to suit your pupils' needs...