Volume and surface area

Volume is the space inside a 3D shape, measured in cubes (cm³). For any prism, volume = area of the cross-section × length. Surface area is the total area of all the faces.

Key facts

  • Cuboid: volume = length × width × height.
  • Prism: volume = cross-section area × length.
  • Cylinder: volume = πr²h.
  • Surface area: add the areas of every face (a net helps).

Worked examples

Example 1

Find the volume of a cuboid 5 cm by 4 cm by 3 cm.

  1. Multiply the three lengths. 5 × 4 × 3 = 60
  2. So 60 cm³

Answer: 60 cm³

Example 2

Find the surface area of the same cuboid.

  1. Front and back. 2 × 5 × 3 = 30
  2. Top and bottom. 2 × 5 × 4 = 40
  3. The two ends. 2 × 4 × 3 = 24
  4. Add them. 30 + 40 + 24 = 94 cm²

Answer: 94 cm²