A ball is inscribed in a cube. Find the surface area of the ball if the total surface area of the cube is 1170 / pi cm2.

Let the length of the edge of the cube be equal to X cm.

Then the total surface area of the cube will be equal to:

Scuba = 6 * X ^ 2 = 1170 / n cm2.

X2 = 1170/6 * n = 195 / n cm2. (1).

The surface area of the ball is:

Sball = 4 * n * R ^ 2 = 4 * n * (D / 2) ^ 2 = n * D ^ 2.

The diameter of the ball is equal to the edge of the square in which it is inscribed. D = X see.

Then Sball = n * X ^ 2.

Substitute equation 1 into it.

Sball = n * 195 / n = 195 cm2.

Answer: The surface area of the ball is 195 cm2.