A cylinder with a radius of 6 cm has the same volume as a ball. Find the height of the cylinder

A cylinder with a radius of 6 cm has the same volume as a ball. Find the height of the cylinder, assuming that the radii of the cylinder and the ball are equal.

Let R – the radius of the base of the cylinder and the radius of the sphere, H – the height of the cylinder;

The volume of a cylinder is equal to the product of the area of its base by the height πR ^ 2 * H;

The volume of the ball is 4/3 * πR ^ 3;

By condition, the volumes of the cylinder and the ball are equal, that is, πR ^ 2 * H = 4/3 * πR ^ 3;

Hence H = 4/3 * R = 4/3 * 6 = 8 cm;

Answer: The height of the cylinder is 8 cm.