A ball is inscribed into the cube, the surface area of which is 100 Pi cm². Calculate the volume of the cube.

The area (S) of the surface of the sphere (ball) is equal to the quadruple area of the great circle: S = 4 * π * R ^ 2, where R is the radius of the ball.
According to the condition of the assignment, 4 * π * R ^ 2 = 100 * π cm2 or R2 = 25 cm2, whence R = 5 cm.
Obviously, the side (a) of the cube, in which the ball is inscribed, is equal to a = 2 * R = 2 * 5 cm = 10 cm.
We define the volume (V) of the cube by the formula V = a ^ 3, where a is the side of the cube.
Therefore, V = a3 = (10 cm) ^ 3 = 1000 cm3.
Answer: The volume of a cube is 1000 cm3.