Question

the minute hand of the tower clock is 12 inches long and the hour hand is 9 inches long. on this clock what is the positive difference between the number of inches traveled by the tip of the minute hand and the tip of the hour hand in one hour? express your answer as a decimal in terms of pi.

Answer 1

consider 12:00 am , the hands will coincide.
In on hour the minute hand makes one rotation, or 2πr inches
= 2π(12) or 24π inches
in the same time the hour hand will make 1/12 of a rotation.
distance of hour hand = (1/12)(2π)(9) = 3π/2 inches

So the difference = 24π - 3π/2 = 45π/2 inches

Answer 2

circumference of hour hand circle = 2 pi *9
in one hour it goes circumference / 12
so
distance = 18 pi/12 = 1.5 pi
now the minute hand
circumference = 2 pi * 12
it goes all the way around so
answer = 24 pi - 1.5 pi = 22.5 pi

Answer 3

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