Volume of a cuboid and a cube

Volume of a cuboid and a cube

Volume of a cuboid and a cube

Volume is "how much fits inside the solid". We measure it in cubic units (cm³, dm³, m³).

Cuboid

A cuboid has three edges `a`, `b`, `c`. Its volume is:

V = a · b · c

Example. A cuboid `5 × 4 × 3` cm: V = `5 · 4 · 3 = 60 cm³`.

Cube

A cube is a special cuboid with all edges equal.

V = a³

Example. A cube with edge 5 cm: V = `5³ = 125 cm³`.

Picture it with "little cubes"

Imagine a cuboid built from 1 cm³ cubes. If it has dimensions 5 × 4 × 3 cm, it's made of 60 cubes — that's its volume.

Checks

  • The volume grows cubically. If you double all the edges, the volume doesn't double — it grows 8 times (2³).
  • For a cube: if you want the edge from the volume, take the cube root: `a = ∛V`.
  • The unit is always cubic (cm³, dm³, m³), never square.

Try it yourself