Question

The area of a sector of a circle bounded by an arc of length 5πcm is equal to 20π sq.cm .Find the radius.​

Answer 1

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 π sq. cm^2

=====> θ / 360 × 2πr = 5π & θ / 360 × πr^2 = 20 π

=====> θ / 360 × πr^2 / θ / 360 × 2πr^2 = 20π / 5π

=====> r / 2 = 4

===> r = 8 cm

We have Area = 1 / 2 lr ===> 20 π = 1 / 2 × 5 π × r = 8 cm

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