Volume of a Cuboid and Cube

A cuboid is a 3D shape with six rectangular faces, like a box or a brick. It has 12 edges and 8 corners, and opposite faces are the same size. A cube is a cuboid whose edges are all equal. In the US a cuboid is usually called a rectangular prism.

The volume of a cuboid is length × width × height. Multiply the three measurements and give the answer in cubic units such as cm³ or m³. A cuboid 5 cm long, 3 cm wide and 2 cm high has volume 5 × 3 × 2 = 30 cm³. A cube is a cuboid with equal edges, so its volume is side × side × side.

A cuboid has 6 faces, 12 edges and 8 vertices, which are its corners. The faces are rectangles, and opposite faces are identical. A cube has the same 6 faces, 12 edges and 8 vertices, but all of its faces are squares. These counts stay the same whatever size the cuboid is.

A cuboid’s length, width and height can all be different. A cube is a special cuboid where every edge is the same length, so every cube is a cuboid. Both use length × width × height; for a cube that is side × side × side, so a 5 cm cube has volume 5 × 5 × 5 = 125 cm³.

Volume is measured in cubic units, because it fills three dimensions: cubic centimetres (cm³) for small objects and cubic metres (m³) for large ones. Liquids are often measured in litres, and 1 litre = 1,000 cm³. In the lesson’s example, a container of 50 × 30 × 20 = 30,000 cm³ holds 30 litres.

Volume is the space inside a 3D shape. Start with a box: count how many 1 cm cubes fit along its length, width and height, then multiply the three numbers. A box 5 cubes long, 3 wide and 2 high holds 5 × 3 × 2 = 30 cubes, so its volume is 30 cm³.