The generatrix of the cone is 20 cm, the total surface area is 400 cm, find the angle of the sweep of the cone.

The total surface area of the cone is:

Sпов = Sсн + Sbok = π * R ^ 2 + π * R * OA.

400 = π * R ^ 2 + π * R * 20.

3.14 * R ^ 2 + 62.8 * R – 400 = 0.

Having solved the quadratic equation, we get R = 5.08 cm.

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

Side = π * R * AO = π * 5.08 * 20 = π * 101.6 cm2.

Also S side = Ssec = π * AO ^ 2 * α / 360 = π * 101.6 cm2.

400 * α = 360 * 101.6.

α = 91.44.

Answer: The sweep angle of the cone is 91.44.