Question

. An arc of a circle is of length 5π cm and the sector it bounds,has an area of 25cm². The radius of the circle is​

Answer 1

Answer:

ANSWER

Let the radius of the circle be r cm and the arc Ab of length 5π cm subtends abgle θ at the centre O of the circle. Then ,

Arc AB=5 π cm and Area of sector OAB=20 πcm

2

⇒

360

θ

×2πr=5πand

360

θ

×πr

2

=20π

⇒

360

θ

×2πr

360

θ

×πr

2

=

5π

20π

⇒

2

r

=4

⇒ r=8cm

We have Area =

2

1

lr⇒20π=

2

1

×5π×r⇒r=8cm