Question

An arc of a circle is of length 5π cm and the sector bounded around it has an area of 20π sq cm. Find the radius of the circle.

Answer 1

Let the radius of the circle be 'r' cm. Given : Length of an arc of the circle = 5π cm and area of the sector = 20π cm² We know that, length of an arc of the circle = θ(2πr)/360° Therefore, θ(2πr)/360° = 5π ⇒ θr = 180*5 ⇒ θr = 900 ⇒ θ = 900/r .........(1) And, Area of the sector = πr²θ/360° Therefore, πr²θ/360° = 20π ⇒ r²θ = 360*20 ⇒ r²θ = 7200 ...........(2) Substitute value of θ from equation (1) in the equation (2), we get ⇒ r²(900/r) = 7200 ⇒ r = 7200/900 ⇒ r = 8 cm