The cylinder is described near the ball. The volume of the sphere is 8 cm3. Find the volume of a cylinder.

In order to obtain the volume of a cylinder, it is necessary to multiply the area of its base by the height:

V = Sb. H = πr ^ 2h.

Since the cylinder is described around the ball, its height is equal to the diameter of the given ball, and the diameter of the cylinder is equal to the diameter of the ball.

Having its volume, we can find the radius:

V = 4/3 π R ^ 3;

R3 = 3V / 4π;

R3 = 3 * 8/4 * 3.14 = 24 / 12.56 = 1.91;

R = ∛1.91 = 1.24 cm.

The diameter of the ball is twice the radius:

d = h = 2R;

d = h = 2 * 1.24 = 2.48 cm.

Now let’s find the volume of the cylinder:

V = 3.14 * 1.242 * 2.48 = 3.14 * 1.54 * 2.48 = 11.992 ≈ 12 cm3.

Answer: the volume of the cylinder is 12 cm3.