# A cube with an edge equal to the square root of 3 is inscribed in a ball. Find the surface area of the ball.

July 22, 2021 | education

| Data: a – edge of the taken cube (a = √3 units).

To find out the required surface area of the ball in question, we will use the formula: Sх = 4 * Π * R ^ 2 = 4 * Π * (d / 2) 2 = 4 * Π * (a * √3 / 2) ^ 2 = 4 * Π * a ^ 2 * 3/4 = 3 * Π * a ^ 2.

Let’s perform the calculation: Sх = 3 * Π * a ^ 2 = 3 * Π * √3 ^ 2 = 9Π units2 ≈ 28.26 units2.

Answer: The surface area of the ball under consideration is 9Π units2 (28.26 units2).

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