1953 AHSME Problems/Problem 11

A running track is the ring formed by two concentric circles. It is $10$ feet wide. The circumference of the two circles differ by about: $\textbf{(A)}\ 10\text{ feet} \qquad \textbf{(B)}\ 30\text{ feet} \qquad \textbf{(C)}\ 60\text{ feet} \qquad \textbf{(D)}\ 100\text{ feet}\\ \textbf{(E)}\ \text{none of these}$

Solution

Call the radius of the outer circle $r_1$ and that of the inner circle $r_2$ . The width of the track is $r_1-r_2$ . The circumference of a circle is $2\pi$ times the radius, so the difference in circumferences is $2\pi r_1-2\pi r_2=10\pi$ feet. If we divide each side by $2\pi$ , we get $r_1-r_2=\boxed{5}$ feet.

1953 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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1953 AHSME Problems/Problem 11

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