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

Imagine a cutaway ball in a cube. It turns out a circle inscribed in a square. The center of the circle coincides with the center of the cube, and, therefore, the radius of the circle, equal to 10 cm, is equal to half of the side of the square. From this it follows that the side of the square and the cube is 20 cm. Let’s use the formula for calculating the volume of a cube. V = a * b * c, where a = b = c = 20 cm V = 20 ^ 3 = 8000 (cm ^ 3).