Cuboids

Volume

Each of the small cubes in this shape has a volume of 1 cm3. The volume of the cuboid is 12 cm3.

12 cube cuboid

It can be calculated by counting the cubes inside or by multiplying the length, width and height together.

Volume = 2 \times 3 \times 2 = 12~\text{cm}^3

\text{volume of a cuboid} = \text{length (l)} \times \text{width (w)} \times \text{height (h)}

Cuboid with w, l and h labelled

Surface area

The surface area of a cuboid can be calculated by adding together the areas of the six faces. The opposite faces of a cuboid are the same sized rectangles, so find the total area of the three different faces, then double to find the total surface area.

Question

Find the surface area of a cuboid of length 4 cm, width 2 cm and height 3cm.

View of a cuboid and its measurements in order to find the surface area

The three different faces of the cuboid are labelled A, B and C

Area of A = 4 \times 3 = 12~cm^2

Area of B = 2 \times 3 = 6~cm^2

Area of C = 4 \times 2 = 8~cm^2

The area of the three faces is 12 + 6 + 8 = 26~cm^2. The total surface area is therefore 26 \times 2 = 52~cm^2.