Surface area of a cube

Topic guide

What this worksheet practises

This worksheet provides practice on calculating the total surface area of a cube. Surface area is the total area of all the outside faces of a 3D shape, like wrapping paper covering a box. A cube is the simplest 3D shape because every single face is exactly the same.

Key method

A cube is made up of exactly 6 identical square faces.

• Identify the length of one side of the cube. (In a cube, the length, width, and height are all the same number).
• Calculate the area of just one of the square faces. (Area of a square = base × height).
• Because a cube has 6 identical faces, multiply the area of that single face by 6 to get the total surface area.
• Write the units correctly. Because it is an area, the units must be squared (e.g. cm², m²).

Worked example

Calculate the surface area of a cube with a side length of 5cm.

Step 1: Find the area of one face.

The face is a square with sides 5cm by 5cm.

Area = 5 × 5 = 25 cm².

Step 2: Multiply by 6 because there are 6 identical faces.

25 × 6 = 150.

The total surface area is 150 cm².

Common mistakes to avoid

The most common mistake is calculating the volume instead of the surface area. A student might see a cube with side length 5 and automatically do 5 × 5 × 5 = 125. This tells you how much space is inside the cube, not the area of its outside faces. Always read the question carefully.

Things to remember

Sometimes a question will tell you the total surface area and ask you to work backwards to find the side length. If the total surface area is 54 cm², you would divide by 6 first (54 ÷ 6 = 9 cm² per face), and then square root that number to find the side length (√9 = 3cm side length).