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 is asking to calculate the total surface area of a cube with a side length of 0.7 metres. To find the total surface area, we will apply the formula for the surface area of a cube, which is 6 times the square of the side length. Since the final answer needs to be provided in square centimetres, we will convert the side length from metres to centimetres before performing the calculation.
Answer
The total surface area of the cube is \( 29400 \text{ cm}^2 \).
Answer for screen readers
The total surface area of the cube is ( 29400 \text{ cm}^2 ).
Steps to Solve
-
Convert the side length to centimetres The side length of the cube is given in metres as 0.7 m. To convert this to centimetres, use the conversion factor: $$ 1 \text{ m} = 100 \text{ cm} $$ Thus, $$ 0.7 \text{ m} = 0.7 \times 100 = 70 \text{ cm} $$
-
Apply the surface area formula The formula for the total surface area ( A ) of a cube is given by: $$ A = 6s^2 $$ where ( s ) is the length of a side of the cube. Substituting ( s = 70 \text{ cm} ): $$ A = 6 \times (70)^2 $$
-
Calculate the square of the side length Calculate ( (70)^2 ): $$ (70)^2 = 4900 $$
-
Calculate the total surface area Now, substitute back into the surface area formula: $$ A = 6 \times 4900 = 29400 \text{ cm}^2 $$
The total surface area of the cube is ( 29400 \text{ cm}^2 ).
More Information
The surface area of a cube is useful in various applications, including packaging, architecture, and understanding three-dimensional objects.
Tips
- Forgetting to convert units: Ensure all measurements are in the same unit before performing calculations.
- Miscalculating square values: Double-check the calculations for squaring numbers, as it's a common source of error.
AI-generated content may contain errors. Please verify critical information
