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If the circle above has center O and circumference 18Ï€, the

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by Brent@GMATPrepNow » Mon Sep 10, 2018 5:42 am
AAPL wrote:Official Guide

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If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9$$
$$B.\ 3\pi+18$$
$$C.\ 6\pi+9$$
$$D.\ 6\pi+18$$
$$E.\ 6\pi+24$$
OA B.
The circle has circumference 18Ï€
circumference = (2)(radius)(Ï€)
So, (2)(radius)(Ï€) = 18Ï€
Solve to get: radius = 9

So, OR = 9 and OT = 9

Now, we'll deal with arc RST
Here the sector angle = 60°
60°/360° = 1/6
So, the arc RST represents 1/6 of the ENTIRE circle
Since the ENTIRE circle has circumference 18Ï€, the length of arc RST = (1/6)(18Ï€) = 3Ï€

So, the perimeter of sector RSTO = 9 + 9 + 3Ï€
= 18 + 3Ï€

Answer: B

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by fskilnik@GMATH » Mon Sep 10, 2018 10:07 am
AAPL wrote:Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9 \,\,\,\,\,\,\,\, B.\ 3\pi+18 \,\,\,\,\,\,\,\, C.\ 6\pi+9 \,\,\,\,\,\,\,\, D.\ 6\pi+18 \,\,\,\,\,\,\,\, E.\ 6\pi+24$$
\[\left. \begin{gathered}
?\,\,\, = \,\,\,2R + \frac{{60}}{{360}}\left( {2\pi R} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\boxed{\,\,? = 2R\,\,\left( {1 + \frac{\pi }{6}} \right)\,\,\,}\,\,\, \hfill \\
2\pi R = 18\pi \,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi } \,\,\,\,2R = 18 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,\underleftrightarrow {18\left( {1 + \frac{\pi }{6}} \right)}\,\, = \,\,18 + 3\pi \]

Please note that even in a trivial problem like this one, we never forget the main motto of our method:

Present FOCUS and DATA in an structured way and CONNECT them as soon as possible!

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by Scott@TargetTestPrep » Wed Apr 10, 2019 4:58 pm
AAPL wrote:Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9$$
$$B.\ 3\pi+18$$
$$C.\ 6\pi+9$$
$$D.\ 6\pi+18$$
$$E.\ 6\pi+24$$
OA B.
We see that the perimeter of sector RSTO consists of 2 radii of the circle and arc RST.

Since the circumference of the circle O is 18Ï€, its radius must be 9. Since the angle measure of sector RSTO is 60 degrees, the length of arc RST must be 1/6 of the circumference of the circle (notice that 60 degrees is 1/6 of 360 degrees). Therefore, arc RST has a length of 1/6 x 18Ï€ = 3Ï€. So the perimeter of sector RSTO is

3Ï€ + 9 + 9 = 3Ï€ + 18

Answer: B

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