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.
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