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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.

 

 Feb 17, 2021
 #1
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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°

 

 

cool cool cool

 Feb 17, 2021

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