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 length of a side of the cube
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Answer
The length of the diagonal (d) of a cube can be calculated using the formula:
d=a3
where 'a' is the length of a side. Given that the diagonal is 25 cm, we can rearrange the formula to solve for 'a':
a = \frac{d}{\sqrt{3}} = \frac{25}{\sqrt{3}} \approx 14.434 \text{ cm}
Step 2
Calculate the total surface area of the cube
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Answer
The total surface area (A) of a cube is given by the formula:
A=6a2
Substituting the value of 'a' we calculated:
A=6(14.434)2≈1250 cm2
