Find the area of the lateral and total surfaces of a cylinder if its height is 10 and its diameter is 12.

The radius of the circle at the base of the cylinder is: R = D / 2 = 12/2 = 6 cm.

Let us determine the area of the lateral surface of the cylinder. Side = 2 * π * R * h = 2 * π * 6 * 10 = 120 * π cm2.

Determine the area of the base of the cylinder. Sb = π * R2 = 36 * π cm2.

Then the total surface area is equal to:

Sпов = 2 * Sсн + S side = 2 * 36 * π + 120 * π = 192 * π cm2.

Answer: The lateral surface area is 120 * π cm2, the total area is 192 * π cm2.