The cube shown has side length 0.7 metres. Work out the total surface area of the cube. Give your answer in square centimetres.
Understand the Problem
The question asks us to calculate the total surface area of a cube with a given side length of 0.7 metres. To solve this, we will use the formula for the surface area of a cube, which is 6 times the side length squared. Since the side length is given in metres, we will convert our final answer to square centimetres.
Answer
The total surface area of the cube is \( 29,400 \, \text{cm}^2 \).
Answer for screen readers
The total surface area of the cube is ( 29,400 , \text{cm}^2 ).
Steps to Solve
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Calculate the surface area formula The formula to find the total surface area ( A ) of a cube is given by: $$ A = 6s^2 $$ where ( s ) is the side length of the cube.
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Substitute the side length Substituting the given side length of 0.7 metres into the formula: $$ A = 6 \times (0.7)^2 $$
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Calculate ( (0.7)^2 ) First, calculate the square of the side length: $$ 0.7 \times 0.7 = 0.49 $$
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Calculate total surface area Now substitute ( 0.49 ) back into the area formula: $$ A = 6 \times 0.49 = 2.94 , \text{m}^2 $$
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Convert square metres to square centimetres Since ( 1 , \text{m}^2 = 10,000 , \text{cm}^2 ), convert ( 2.94 , \text{m}^2 ) to square centimetres: $$ 2.94 \times 10,000 = 29,400 , \text{cm}^2 $$
The total surface area of the cube is ( 29,400 , \text{cm}^2 ).
More Information
The total surface area represents the sum of the areas of all the faces of the cube. A cube has 6 faces, and each face is a square, which explains why we use the formula ( A = 6s^2 ).
Tips
- Not squaring the side length correctly.
- Forgetting to convert square metres to square centimetres, which is essential when the final answer must be in a different unit.
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