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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.

 Jun 14, 2019
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The tip of the hour hand travels the circumference of its circle once every 12 hours.

24 hours / 12 hours  =  2     So the hour hand travels its circumference 2 times per day.

 

The tip of the minute hand travels the circumference of its circle once every 1 hour.

24 hours / 1 hour  =  24     So the minute hand travels its circumference 24 times per day.

 

circumference of hour hand circle  =  2π( 5 cm )  =  10π cm

circumference of minute hand circle  =  2π( 10 cm )  =  20π cm

 

distance traveled by tip of hour hand  =  2 * 10π cm  =  20π cm

distance traveled by tip of minute hand  =  24 * 20π cm  =  480π cm

 

20π cm + 480π cm   =   500π cm   =   5π  meters   ≈   15.708 meters

 Jun 14, 2019

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