Question

Find the area of the sector of a circle of radius 42 cm and of central angle 30°. Also, find the area of the corresponding major sector. `["Use"  π = 22/7]`

Answer 1

Given:

Radius (r) = 42 cm

Central angle (θ) = 30°

Area of minor sector:

Area = `θ/360^circ xx πr^2`

Area = `30/360 xx 22/7 xx 42 xx 42`

Area = `1/12 xx 22 xx 6 xx 42`

Area = `1/2 xx 22 xx 42`

Area = 11 × 42

Area = 462 cm²

Area of major sector:

Area = Total area of circle – Area of minor sector

Area = πr² – 462

Area = `(22/7 xx 42 xx 42) - 462`

Area = (22 × 6 × 42) – 462

Area = 5544 – 462

Area = 5082 cm²