Maths Olympiad Prep

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Geometry Difficulty 2.1 Junior Find the answer

The number of revolutions of a wheel, with fixed center and with an outside diameter of 66 feet, required to cause a point on the rim to go one mile is:

Pick one

Solution

We know that the radius of the wheel is 33 feet, so the total circumference of the wheel is 6π6\pi feet. We also know that one mile is equivalent to 52805280 feet. It takes 52806π\frac{5280}{6\pi} revolutions for any one point on the wheel to travel a mile. Simplifying, we find that the answer is (C) 880π\boxed{\textbf{(C) } \frac{880}{\pi}}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.