Question

Find the ratio between the radius and slant height of a cone by roiling up a sector with central angle 120°. If the curved surface area is 108 π, find the radius and slant height of the cone.

Answer 1

Area of the sector with central angle 120° is one-third of the area of the circle.

Curved surface area = 108 π

Ares of die; sector = 108 π,

which is one-third of the area of the circle

Area of the circle = 108 π × 3

πr² = 324 π

Radius of the circle r = 18 cm

Slant height = 18 cm

Radius of the cone = 6 cm