The area of the lateral surface of the cone is 240п cm2, and the angle in its scan is 120 degrees.

The area of the lateral surface of the cone is 240п cm2, and the angle in its scan is 120 degrees. Calculate the total surface area of the ball.

The lateral surface area is equal to the area of the circular sector.
Sside = π * L ^ 2 * α / 360.
240 * π = π * L ^ 2 * 120/360.
L ^ 2 = 360 * 240/120 = 720.
L = 12 * √5 cm.
Also S side = π * R * L.
240 * π = π * R * 12 * √5.
R = 240/12 * √5 = 20 / √5 = 4 * √5 cm.
Then Sпов = π * R * (L + R) = π * 4 * √5 * (12 * √5 + 4 * √5) = 340 * π cm2.
Answer: The surface area of the cone is 340 * π cm2.