We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
54
1
avatar

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
 #1
avatar+8406 
+2

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

6 Online Users

avatar