Cuboids
Volume
Check out the refreshed revision resources for GCSE Maths: Cubes and cuboids, with step-by-step slideshows, quizzes, practice exam questions, and more!
Each of the small cubes in this shape has a volume of 1 cm3. The The volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml. of the cuboid is 12 cm3.
It can be calculated by counting the cubes or by multiplying the three lengths together.
Volume = \(2 \times 3 \times 2 = 12~\text{cm}^3\)
\(\text{volume of a cuboid} = \text{length (l)} \times \text{width (w)} \times \text{height (h)}\)
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.
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 of the six faces is therefore \(26 \times 2 = 52~cm^2\).
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