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The length of the longest diagonal of a cube is 25 cm - OCR - GCSE Maths - Question 14 - 2019 - Paper 6

Question 14

The length of the longest diagonal of a cube is 25 cm. Calculate the total surface area of the cube.

Worked Solution & Example Answer:The length of the longest diagonal of a cube is 25 cm - OCR - GCSE Maths - Question 14 - 2019 - Paper 6

Step 1

Calculate the side length of the cube

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Answer

The diagonal of a cube can be calculated using the formula: $d = a\\sqrt{3}$ , where $d$ is the diagonal and $a$ is the side length of the cube. Given that the diagonal $d = 25$ cm, we can rearrange this formula to solve for $a$ : $a = \frac{d}{\\sqrt{3}} = \frac{25}{\\sqrt{3}} \approx 14.43 \text{ cm}$ .

Step 2

Calculate the total surface area of the cube

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Answer

The total surface area (S) of a cube can be calculated using the formula: $S = 6a^2$ . Substituting the value of $a$ we found: $S = 6 \times (14.43)^2 \approx 1249.74 \text{ cm}^2$ . Rounding to the nearest whole number gives us approximately 1250 cm².

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