SOLUTION: the length of an arc of a circle is 12 cm,the corresponding sector area is 108 cm^2. Find the radius of the circle and the angle subtended at the centre of the circle by the arc

Algebra ->  Circles -> SOLUTION: the length of an arc of a circle is 12 cm,the corresponding sector area is 108 cm^2. Find the radius of the circle and the angle subtended at the centre of the circle by the arc      Log On


   

Question 739871: the length of an arc of a circle is 12 cm,the corresponding sector area is
108 cm^2.
Find the radius of the circle and the angle subtended at the centre of the circle by the arc.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What if the area were extended to the whole circle, pi%2Ar%5E2, and the arc were extended to the whole circumference, 2%2Api%2Ar? The comparison of area to arc is %28pi%2Ar%5E2%29%2F%282%2Api%2Ar%29=r%2F2. That should be the same for the area of a sector and its arc.

Using that ratio, we can make a proportion,
r%2F2=108%2F12, and we can easily find highlight%28r=2%2A108%2F12%29, simplify.....!