A cube is inscribed in a ball, find the surface area of the ball if the edge of the cube is equal to √6dm.
| April 30, 2021 | education
Since the cube is inscribed in a ball, the diagonal of the cube is equal to the diameter of the ball.
The diagonal of the cube (the diameter of the ball) is calculated by the formula:
2 * R = √ (a² + b² + c²),
2 * R = √ (6 + 6 + 6) = 6√6,
R = 3√6.
The surface area of the ball is calculated by the formula:
S = 4 * pi * R² = 4 * pi * 9 * 6 = 216 * pi.
Answer: the surface area of the ball will be equal to 216 * pi units ².
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