Question

In the picture the central angles of both the sectors are equal. Sum of the radii of the sectors is 18 cm.

Area of the shaded part is 18 π cm² . Find the radii of the sector.

Answer 1

‘Let ‘r’ be the radius of the small sector and ‘R’ be the radius of the large sector. 

R + r = 18 …………. (1)

Area of the shaded portion = Area of the large sector – area of the small sector

From this 2R = 26,

∴ R = 13 cm

also 2r = 10,

∴ r = 5 cm