Question 1104866: How far does the tip of the second hand of a clock move in 25 seconds if its length is 7 cm? Express your answer in terms of pi.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the second hand makes one full revolution in 60 seconds.
therefore, in 25 seconds, it's made 25/60 = 5/12 of a revolution.
since the circumference of a circle is 2 * pi * r, when r = 7, the circumference of the circle is 14 * pi.
since the second hand has traversed 5/12 of a complete circle, then it has moved 5/12 * 14 * pi centimeters in 25 second.
that becomes 35 / 6 * pi centimeters.
the tip of the second hand has moved 35/6 * pi centimeters in 25 seconds.
as a test to see if this makes sense, 1 second it has moved 1/60 * 14 * pi = 14/60 * pi centimeters.
multiply 1/60 * 14 * pi by 60 and it has moved 14 * pi centimeters in 60 seconds.
multiply 1/60 * 14 * pi by 25 and it has moved 25 / 60 * 14 * pi = 5/12 * 14 * pi = 5/6 * 7 * pi = 35/6 * pi centimeters.
it all seems to check out so i would go with 35/6 * pi centimeters.
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