Question

Find the radius of a sector whose are length and area are 27.5 cm and 618.75 cm?



respectively



(a) 35 cm (b) 25 cm



45 cm (d) 55 cm

Answer 1

area of a sector=1/2×r×l
618.75=1/2×r×27.5
r=618.75/13.75=45cm

Answer 2

Dear Student,

◆ Answer -

r = 55 cm

● Explaination -

Let r be radius of the circle and θ be subtended angle.

Area of sector,

A = πr^2 × θ/360

618.75 = πr^2 × θ/360 ...(1)

Length of arc,

l = 2πr × θ/360

27.5 = 2πr × θ/360 ...(2)

Divide (1) by (2),

618.75 / 27.5 = (πr^2 × θ/360) / (2πr × θ/360)

r/2 = 22.5

r = 22.5 × 2

r = 55 cm

Hence, radius of a sector is 55 cm.

Thanks dear. Hope this helps you...