Volume of a Cuboid

GCSE Geometry volume cuboid
Practice this formula All formulas
\( V=\ell\,w\,h \)

Statement

The volume of a cuboid (a 3D box shape) is found by multiplying its three dimensions: length, width, and height.

\[ V = lwh \]

This formula works for any rectangular box where all faces are rectangles.

Why it’s true

  • Area of the base rectangle = length × width.
  • Volume = base area × height.
  • So volume = (l × w) × h = lwh.

Recipe (how to use it)

  1. Identify the three dimensions: length, width, height.
  2. Multiply them together.
  3. Include units (cm³, m³, etc.).

Spotting it

Look for 3D box shapes in questions with dimensions given.

Common pairings

  • Surface area problems (different formula).
  • Unit conversions (cm³ to m³, litres, etc.).

Mini examples

  1. Given: l=5 cm, w=3 cm, h=2 cm. Find: Volume. Answer: 30 cm³.
  2. Given: l=10 m, w=4 m, h=2 m. Find: Volume. Answer: 80 m³.

Pitfalls

  • Mixing up surface area and volume.
  • Forgetting units should be cubic.
  • Misreading one side as slanted when it’s actually vertical.

Exam strategy

  • Write the formula before substituting values.
  • Double-check all units are consistent.
  • If dimensions are given in mixed units, convert first.

Summary

The volume of a cuboid is simply the product of its length, width, and height. Always remember to cube the units when presenting your answer.