SOLUTION: The hour hand of a clock has length 10cm. How far does its tip travel in 3 hours and 15 minutes? Please provide a solution to the answer. Thank you.

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Question 1038801: The hour hand of a clock has length 10cm. How far does its tip travel in 3 hours and 15 minutes? Please provide a solution to the answer. Thank you.
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Think of the clock face traversed by the hour hand as a circle. The formula for the circumference of a circle is:
c=2%28pi%29r
So the circumference of the circle formed by the entire clock face is:
c=2%28pi%2910
c=20%28pi%29
But you are asked for the fraction of this full circumference traveled in 3 hours and 15 minutes. This fraction is equal 3*60+15=195 minutes. Whereas the entire circumference is 12*60=720 minutes. So the fraction (call it f) is:
f=195%2F720
Reducing...
f=13%2F48
The distance traveled (d) is this fraction of what we originally found for the full circumference:
d=f%2Ac
d=%2813%2F48%29%2A20%28pi%29
Simplifying...
highlight%28d=%2865%28pi%29%2F12%29%29
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Good Luck,
tutor_paul@yahoo.com