Question

From a circle of radius 15 cm, a sector with angle 216° is cut out and its bounding radii are bent so as to form a cone. Find its volume.

Answer 1

Radius of the sector, ‘r’ = 15 cm 

Angle of the sector, ‘x’ = 216°

∴ Length of the arc, l = x/360 x 2πr

= 216/360 2πr = 3/5 (2πr)

Perimeter of the base of the cone = Length of the arc

2πr of cone = 6/5 πr of the circle

Radius of the cone ‘r’ = 3/5 x 15 = 9

Radius ‘r’ of the circle = slant height l of the cone = 9 cm

= 1018.3 cm³