1953 AHSME Problems/Problem 11

A running track is the ring formed by two concentric circles. If the circumferences of the two circles differ by $10\pi$ feet, how wide is the track in feet?

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

Solution

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