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

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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)   (Show Source): You can put this solution on YOUR website!
What if the area were extended to the whole circle, , and the arc were extended to the whole circumference, ? The comparison of area to arc is . That should be the same for the area of a sector and its arc.

Using that ratio, we can make a proportion,
, and we can easily find , simplify.....!

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