The minute hand on a clock is 5 inches long and moves from 12 minutes to 42 minutes. Find the exact value of how far did the tip of the minute hand moves?

Question

The minute hand on a clock is 5 inches long and moves from 12 minutes to 42

minutes. Find the exact value of how far did the tip of the minute hand moves?

Answer 1

42-12 = 30. the minute hand moved half way around the clock, covering the edge of a semi-circle

the full circle's circumference = 2pi(r) = 2pi(5) = 10pi

divide by 2: 10pi/2 = 5pi = about 15.7

Answer 2

The minutes passed will be

42-12 = 30.minutes which is 180 degrees. One way is to say that we just need half of the circumference of the circle which is 2 pi r / 2 = 2 * 5 * pi / 2 which is 5 pi as Raymond did correctly. Another way is using the formula (in case it was not exactly 30 minutes or 180 degrees)

The formula for the arc length is:

l = r * a (which a is the angle in radians. If we change 180 degrees to radian (Degree /180 = Radians / pi) it will be pi radians (half circle, the whole circle is 2 pi radians). We know r = 5 and a is pi, so

l = 5 * pi which is almost 15.7 inches.