The radius of the cylinder base is 8cm. The area of the lateral surface of the cylinder is half the area

The radius of the cylinder base is 8cm. The area of the lateral surface of the cylinder is half the area of the base. Find the volume of a cylinder

Since the radius of the base of the cylinder is 8 cm, the area of the base is:

S = π * r² = 64 * π (cm²).

As you know, the area of the lateral surface of the cylinder is equal to:

S = 2 * π * r * h.

This means that the lateral surface area of this cylinder is equal to:

S = 2 * π * 8 * h

S = 16 * π * h (cm²).

By the condition of the problem, we get:

2 * 16 * π * h = 64 * π,

32 * π * h = 64 * π,

h = 2 (cm).

The volume of the cylinder is: V = π * r² * h.

V = π * 64 * 2 = 128 * π (cm³).

Answer: V = 128 * π cm³.