The ratio of the volume of the cylinder to the volume of the ball inscribed in it is.

Let the radius of the ball be R cm.

Since the ball is inscribed in a cylinder, the radius of the base of the cylinder is equal to the base of the ball, and the generatrix of the cylinder is equal to the diameter of the inscribed ball. L = 2 * R.

Let’s define the volume of the ball.

Vsh = 4 * π * R ^ 3/3 cm3.

Determine the area of the base of the cylinder.

Sb = π * R ^ 2 cm2.

Then the volume of the cylinder is: Vc = Sax * L = π * R ^ 2 * 2 * R = 2 * π * R ^ 3 cm3.

Let us find the ratio of the volume of the cylinder to the volume of the sphere.

Vts / Vsh = (4 * π * R ^ 3/3) / 2 * π * R ^ 3 = 2/3.

Answer: The ratio of volumes is 2/3.