Пошаговое объяснение:
The surface area of the base of the cylinder is given by the formula: A = πr^2, where r is the radius of the base. Since the diameter of the base is 8, the radius is half of that, so r = 8/2 = 4. Plugging this value into the formula, we have:

A = π(4^2) = 16π.

The volume of the cylinder is given as 64π, which can be expressed as V = πr^2h, where h is the height of the cylinder. We need to find the value of h. Rearranging the formula, we have:

64π = π(4^2)h

64 = 16h

h = 64/16

h = 4.

So, the height of the cylinder is 4 units.

The lateral surface area of a cylinder is given by the formula: A = 2πrh. Substituting the known values, we have:

A = 2π(4)(4) = 32π.

Therefore, the area of the lateral surface of the cylinder is 32π square units.