A ball is inscribed in a cube. Find the ratio of the areas of the surfaces of the cube and the ball.

Let the length of the edge of the rhombus be X cm. AB = AA1 = AD = X cm.

Then the volume of the cube will be equal to:

Vcube = X ^ 3 cm3.

Since the ball is inscribed in a cube, the diameter of the ball is equal to the length of the edge of the cube.

D = KN = AB = X cm.

The volume of the ball is:

Vball = 4 * n * R ^ 3/3 = 4 * n * (D / 2) ^ 3/3 = (4 * n * D ^ 3) / 8/3 = n * X ^ 3/6.

Then: Vcube / Vball = X ^ 3 / (n * X ^ 3/6) = 6 / n.

Answer: The area of a cube refers to the area of the ball as 6 / p.