Find the area of the lateral surface of the cone if its axial section is a right-angled triangle, the leg of which is 10 cm.

The axial section of the cone is an isosceles triangle ABC. By condition, triangle ABC is rectangular, then AB = BC, angle ABC = 90.

By the Pythagorean theorem, AC^2 = 2 * AB^2 = 100 * 2.

AC = 10 * √2 cm.

The BO segment is the height and median of the ABC triangle, then AO = R = AC / 2 = 10 * √2 / 2 = 5 * √2 cm.

Let us determine the area of the lateral surface of the cone.

Side = Side = π * R * L = π * AO * BO = π * 5 * √2 * 10 = 50 * √2 * π cm2.

Answer: The area of the lateral surface of the cone is 50 * √2 * π cm2.