The total surface area of the cube is 60 cm2, find the length of the diagonal of the cube face.
| September 10, 2021 | education
1. By the statement of the problem, it is known that the total surface area of a cube is 60 cm².
2. We know that each face of the cube is a square, and there are 6 faces, then the formula for a given value will be written as
60 cm² = 6 * a * a = 6 * a², where a is an edge, the length of which is defined as √60: 6 = √10 cm.
The diagonal d of the face is calculated by the Pythagorean theorem:
d² = a² + a² = 2 a², whence d = √2 * 10 cm = √20 cm = √ 4 * 5 = 2 √5 cm.
Answer: The length of the diagonal of a cube face is 2 √5 cm.
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