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In the figure above, a 100-meter long circular running
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Updated on: 22 Mar 2019, 11:39
Updated on: 22 Mar 2019, 11:39
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#GREpracticequestion In the figure above, a 100-meter long circular running track.jpg [ 5.92 KiB | Viewed 1905 times ]
In the figure above, a 100-meter long circular running track is inscribed inside of a square field. Approximately what fraction of the square field is enclosed within the circular track?
A. \(\frac{1}{6}\)
B.\(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{5}{6}\)
Re: In the figure above, a 100-meter long circular running
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22 Mar 2019, 07:14
22 Mar 2019, 07:14
pranab01 wrote:
In the figure above, a 100-meter long circular running track is inscribed inside of a square field. Approximately what fraction of the square field is enclosed within the circular track?
The question above is from Manhattan Prep test. I tried to solve but couldn't end up with any options.
Experts plz have a look
Re: In the figure above, a 100-meter long circular running
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22 Mar 2019, 11:51
22 Mar 2019, 11:51
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Expert Reply
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#GREpracticequestion In the figure above, a 100-meter long circular running track.jpg [ 8.12 KiB | Viewed 1879 times ]
The diameter of the circle is = 100 because is the running track itself. However, as you can see from the figure the diameter is also one side of the square.
So, one side of the square is 100 and the area is \(s^2 = 100^2 = 10,000\)
The radius is \(= \pi r^2 = \pi 50^2 = 3.14 * 2,500 \approxeq 7,850\). This is the area of the circle.
Therefore, the area of the circle enclosed into the square is the follow
\(7850 \approxeq \frac{3}{4} of 10,000\).
D is the answer
