Find the area of the lateral surface of the cylinder if its axial section is 10.

The axial section of the cylinder is a rectangle, one of the sides of which is equal to the height of the cylinder, the other to the diameter of the base. This means that the axial section area is equal to the product of the height and the diameter:

S = h * d = 10.

The lateral surface area of the cylinder is equal to the product of the height and the circumference of the base:

Side = h * 2 * π * r = h * π * d.

Since h * d = 10, then S side = 10 * π ≈ 31.4.