Question

An arc of a cicle is of length 5pie cm and sector it bounds has an area of 20pie cm^2.then find its radius.

Answer 1

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 πcm²

$⇒360θ×2πr=5πand360θ×πr2=20π</p><p></p><p></p><p>⇒360θ×2πr360θ×πr2=5π20π</p><p></p><p></p><p>⇒2r=4</p><p></p><p></p><p>⇒    r=8cm </p><p></p><p></p><p>We have  Area = 21lr⇒20π=21×5π×r⇒r=8cm</p><p></p><p>$

Answer 2

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 πcm²

⇒360θ×2πr=5πand360θ×πr2=20π < /p > < p > < /p > < p > < /p > < p > ⇒360θ×2πr360θ×πr2=5π20π < /p > < p > < /p > < p > < /p > < p > ⇒2r=4 < /p > < p > < /p > < p > < /p > < p > ⇒ r=8cm < /p > < p > < /p > < p > < /p > < p > We have Area = 21lr⇒20π=21×5π×r⇒r=8cm < /p > < p > < /p > < p >⇒360θ×2πr=5πand360θ×πr2=20π</p><p></p><p></p><p>⇒360θ×2πr360θ×πr2=5π20π</p><p></p><p></p><p>⇒2r=4</p><p></p><p></p><p>⇒ r=8cm </p><p></p><p></p><p>Wehave Area = 21lr⇒20π=21×5π×r⇒r=8cm</p><p></p><p>