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In the figure shown, O is the center of the circle. If the area of the ... ...

In the figure shown, O is the center of the circle. If the area of the circle is 9π, then the perimeter of the sector PRQO is
(A)    Image – 6
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set J: Geometry

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Posted: 07/20/2012 19:42
Where does the +6 come from?
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Posted: 07/20/2012 20:15
Since the area of the circle is 9π, we get

πr^2 = 9π
r^2 = 9
r = 3

Now, the circumference of the circle is
C = 2πr = 2π3 = 6π

Since the central angle is 30°, the length of arc PRQ is 30° / 360° or 1/12·6π or π/2.

BUT, the perimeter of the section includes OP and OQ, which is just the radius.

So you have to add 3 + 3 to π/2.
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Posted: 07/20/2012 20:59
I swear my brain is melting! Thanks for pulling me back into reality.
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