In the following diagram, a circle has radius r (metres), and angle θ (radians), and centre O.
The area of the shaded sector is 6π/5, and the length of the sector AB is 3π/5.
a) Find the value of r.
b) Find the value of θ.
+128475 Area of sector = (1/2) r^2 (theta)
(6/5)pi = (1/2) r^2 (theta)
(12/5)pi = r^2 (theta)
theta = (12 pi) / (5 *r^2) (1)
Arc length = r (theta)
(3/5) pi = r(theta) (2)
Sub (1) into (2)
(3/5) pi = r (12 pi) / ( 5 * r^2)
(3/5) = (12/5) / r
r = (12/5) /(3/5)
r = 12/3
r = 4
theta = (12/5)pi / 4^2 = (12/80) pi = (3/20)pi = 27°
