SOLUTION: In a figure, the circle has center O and radius 3. If the area of the minor sector AB is between 5 and 10. What's one possible integer value of arc length s that's in middle of AB?

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Question 1089416: In a figure, the circle has center O and radius 3. If the area of the minor sector AB is between 5 and 10. What's one possible integer value of arc length s that's in middle of AB?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I understand that the sector and circle look like the drawing below,
and that the problem asks for one possible integer value for the length of the arc shown in red.

The area of a sector or a circle with radius R
and length of arc or circumference L is
area=R%2AL%2F2 .
(If that reminds you of the formula for area of a triangle, it is not a coincidence).
In this case, we are told that for the sector with arc length AB=L
5%3C3L%2F2%3C10 .
Multiplying all three sides of that inequality times 2%2F3 , we get
5%282%2F3%29%3CL%3C10%282%2F3%29
10%2F3%3CL%3C20%2F3
3%261%2F3%3CL%3C6%262%2F3 .
So, possible integer arc lengths are L=4 or L=5 or L=6 .