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.

Lightning Dec 27, 2018

#1**+3 **

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.

.tertre Dec 27, 2018