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The minute hand of a 12-hour clock measures 10 cm from its tip to the center of the clock face, and the hour hand from its tip to the center of the clock face is 5 cm. What is the sum of the distances, in meters, traveled by the tips of both hands in one 24-hour period? Express your answer to the nearest thousandth of a meter.

 Dec 27, 2018
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We have  2* pi *5=10pi cm in 12 hours, so in 24 hours, that would be 20pi cm. For the minute hand, we have 2 * pi *  10= 20 pi cm. That is only for one revolution, so 20pi*24=480 pi. Thus, the answer is  \(480\pi+20]pi=500\pi\approx\boxed{1570.796}.\) So, that is 15.708 meters.

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 Dec 27, 2018
edited by Guest  Dec 27, 2018
edited by tertre  Dec 28, 2018

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