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83% (01:18) correct
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If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is
(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24
Attachment:
6p5jvHu.jpg [ 10.49 KiB | Viewed 28662 times ]
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21 May 2017, 11:48
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The perimeter of of sector RSTO is (radius OR) + (radius OT) + (minor arc RT).
The circumference is \(18\pi\): \(2\pi{r}=18\pi\) --> \(r=9\);
Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);
So, the perimeter of sector RSTO is (radius OR) + (radius OT) + (minor arc RT) = \(9+9+3\pi=3\pi+18\).
Answer: B.
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sashiim20
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21 May 2017, 19:06
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Circumference = 2\(\pi\)r = 18\(\pi\)
r = \(\frac{18}{2}\) = 9
Perimeter of sector RSTO = Arc Length + r + r
Arc Length = 2\(\pi\)r\(\frac{C}{360}\) (C is central angle of the sector)
C = \(60^{\circ}\)
Arc Length = 2\(\pi\)r\(\frac{60}{360}\) = 2*9*\(\pi\)\(\frac{60}{360}\) = 3\(\pi\)
Therefore Perimeter of sector RSTO = 3\(\pi\) + 9 + 9 = 3\(\pi\) + 18
Answer B...
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