Question

Chapter : Circles 1 question

Answer 1

We can solve this question in 2 ways: either using degrees or converting the degrees into radians.

Since, the question says degrees itself and there is no specification of using radians only, so I have solved it using degrees itself.

Part (a):

Perimeter of sector ORS = 2*Radius + Arc RS = 2*21 +
`60* ( \pi )/(180) *21 = ( \pi )/(3) *21 = 7 \pi`

Part (b):

Area of sector ORS =
`(60)/(360) * \pi * 21^(2) = (1)/(6) * \pi *21*21= (147)/(2) \pi`

Area of sector POQ =
`(36)/(360) * \pi * 14^(2) = (1)/(10) * \pi * 196 = (196)/(10) \pi`

Thus, area of shaded region
= Area of sector ORS - Area of sector POQ

=
`(147)/(2) \pi - (196)/(10) \pi = (735 - 196)/(10) \pi = (539)/(10) \pi = 53.9 \pi`