Find the area of the lateral surface of the cone if the two sides of the axial section of this cone are 4 and 9.

The axial section of the cone is an equilateral triangle ABC. Since from the conditions for constructing triangles, the sum of the lengths of any two of its sides is greater than the third side, the base of the AC of the triangle is 4 cm.

The height of ВO is the median of the triangle ABC, then AO = R = AC / 2 = 4/2 = 2 cm.

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

Side = π * R * L = π * AO * BO = π * 2 * 9 = 18 * π cm2.

Answer: The area of the lateral surface of the cone is 18 * π cm2.