A ball with a radius of 10 cm is placed in a cube so that it touches all its faces. Calculate the volume of the cube.

The ball touches all the faces of the cube, which means that the side of the cube is equal to the diameter of the ball.

Let’s find the diameter of the ball by the formula:

d = 2 * R;

d = 2 * 10 = 20 cm.

Ball diameter = cube side = 20 cm.

Let’s find the volume of the cube by the formula:

V = a ^ 3 = 20 ^ 3 = 20 * 20 * 20 = 8000 cm ^ 3.

Answer: 8000 cm ^ 3.