the area of sector JLK in circle L

Question

area of sector JLK in circle L  is 3 pi inches squared.  Find mJK (arc).

Answer 1

The proportion of that sector's area to the circle's total area is:

 

(3π)/(πr²)

 

The proportion of that arc's length to the circle's total circumference is:

 

mJK/(2πr)

 

 

 

Those proportions should be equivalent. So:

 

(3π)/(πr²) = mJK/(2πr)

(3π)(2πr) = (πr²)mJK

6π²r = (πr²)mJK

(6π²r)/(πr²) = mJK

(6π)/r = mJK

 

 

 

This is why Mark asked what the radius of the circle is... You can't finish the problem without it!