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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 12-hour period? Express your answer to the nearest thousandth of a meter.

 Apr 20, 2021
 #1
avatar+8 
+1

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

 Apr 20, 2021
 #2
avatar+31711 
+1

Hey MHB.... hour hand makes ONE revolution in 12 hours     minute hand makes 12 revs

ElectricPavlov  Apr 20, 2021
 #3
avatar+8 
+1

Okaaaaaaaaaaay, EP

MyHoneyBunches  Apr 20, 2021
 #4
avatar+31711 
+1

Well ...your answer  has hour hand making 2 revs and minute hand making 24 revs....thought you might edit your answer.....

ElectricPavlov  Apr 20, 2021
 #5
avatar+8 
+1

But thats the thing I can't anymore, EP

 Apr 20, 2021
 #6
avatar+31711 
+1

Sorry......you can re-post it though....

 

*** edited ***

distance traveled by tip of hour hand  =  1 * 10π cm  =  10π cm

distance traveled by tip of minute hand  =  12 * 20π cm  =  240π cm

 

     250 pi cm =~ 7.854 meters

ElectricPavlov  Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021

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