The volume of a cylinder circumscribed about a circle is 39, which is the volume of a circle.

Since the cylinder is described around the ball, the height of this cylinder is equal to the diameter of the ball, and the radius of the circle at the base of the cylinder is equal to the radius of the ball.

Sop = π * R ^ 2.

Then Vcyl = Sosn * h = π * R ^ 2 * D = π * R ^ 2 * 2 * R = 2 * π * R ^ 3 = 39 cm3.

Let us express from this expression π * R ^ 3.

π * R ^ 3 = 39/2. (1).

The volume of the ball is:

Vball = 4 * π * R ^ 3 / 3. Substitute equation 1.

Vball = 4 * (39/2) / 3 = 2 * 13 = 26 cm3.

Answer: The volume of the ball is 26 cm3.