The answer I got was $45.8$cm but it seems wrong. I did
$$ A=\pi r^2 $$
$$ 12= \frac{60}{360} \pi r^2 $$
$$ \frac{12}{\pi} \cdot \frac{360}{60}=r=22.9183118 $$
$$ d=45.8 $$
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You could check your answer. $A=\frac 14 \pi d^2$. If we plug in your answer, the area of the circle comes out about $1647.5$, far too large. – Ross Millikan Jan 12 '16 at 22:57
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1It seems you forgot to take the square root of $r^2$... – abiessu Jan 12 '16 at 22:58
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Now that it is formatted, one can see that (besides changing $r$ to $x$ at one point) you lost the square on $r$, so did not take the square root. – Ross Millikan Jan 12 '16 at 22:59
2 Answers
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Assuming that I've accurately transcribed your approach, your error is that you didn't take the square root. You should have $r = \sqrt{\frac{72}{\pi}} \doteq 4.7873$, and then $d \doteq 9.5746$.
Brian Tung
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Between the second and third line you lost the square on $r$, so did not take a square root that you should have.
Ross Millikan
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