Question

Find the central angle of the sectors whose measures are given below. `(π = 22/7)`

area = 462 cm², r = 21 cm

Answer 1

area = 462 cm², r = 21 cm

Radius of the Sector = 21 cm

Area of the sector = 462 cm² 

`"lr"/2` = 462

`("l" xx 21)/2` = 462

l = `(462 xx 2)/21`

l = 22 × 2

Length of the arc l = 44 cm

`(theta^circ)/(360^circ) xx 2pi"r"` = 44 cm

`(theta^circ)/(360^circ) xx 2 xx 22/7 xx 21` = 44 cm

θ° = `(44 xx 360 xx 7)/(2 xx 22 xx 21)`

θ° = 120°

∴ Central angle of the sector = 120°