In a truncated cone with a generatrix 5 cm long, the perimeter of the axial section is 40 cm.

In a truncated cone with a generatrix 5 cm long, the perimeter of the axial section is 40 cm. Find the area of the lateral surface of this cone.

The axial section of the truncated cone is an isosceles trapezoid, the bases of which are the diameters of the bases, and the lateral sides of the generatrix.

Then Ravsd = AB + BC + CD + AD = 5 + 2 * r + 5 + 2 * R = 40 cm.

2 * (R + r) = 30 cm.

(R + r) = 30/2 = 15 cm.

The lateral surface area of the truncated cone is: Sside = π * L * (R + r) = AB * (R + r) = π * 5 * 15 = π * 75 cm2.

Answer: The lateral surface area is π * 75 cm2.