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3D shapes: volume and surface area

Volume is how much space a 3D shape takes up; surface area is the total area of all its faces. For a cuboid (a box shape) both come from just three measurements: length, width and height.

What is tested

  • Volume of a cuboid: length × width × height
  • Surface area: adding the areas of all six faces
  • Counting cubes, and converting cm³ to litres (1,000 cm³ = 1 litre)

Worked example

A box measures 5 cm by 4 cm by 3 cm. Find its volume and its surface area.

  1. Volume = 5 × 4 × 3 = 60 cm³.
  2. The faces come in three matching pairs: 5 × 4 = 20, 5 × 3 = 15 and 4 × 3 = 12 cm².
  3. One of each pair: 20 + 15 + 12 = 47 cm².
  4. Double it for all six faces: 47 × 2 = 94 cm².

Answer: Volume 60 cm³; surface area 94 cm²

Exam-day checklist

  • Volume uses cubic units (cm³); area uses square units (cm²).
  • A cuboid has 6 faces in 3 matching pairs.
  • Make sure all lengths are in the same unit first.
  • 1,000 cm³ = 1 litre.

Common mistakes

  • Adding the three lengths instead of multiplying.
  • Counting only three faces for surface area.
  • Mixing cm and m in one calculation.

Try it yourself

1. How many 1 cm cubes fill a box 6 cm long, 2 cm wide and 3 cm high?

Show answer

36

6 × 2 × 3 = 36 cubes.

2. A fish tank is 50 cm long, 20 cm wide and 10 cm high. How many litres does it hold when full?

Show answer

10 litres

50 × 20 × 10 = 10,000 cm³, and 1,000 cm³ = 1 litre.

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