The minute hand of a clock is 6 inches long
Asked by maham237 @ in Mathematics viewed by 282 People
how far does the tip of the minute hand move in 15 minutes? how far does it move in 25 minutes? round answers to two decimal places.
Answered by maham237 @
This problem involves finding arc lengths. The formula for arc length
is s = r*theta, where r is the radius and theta the central angle.
In 15 minutes, the minute hand sweeps out 1/4 of a circle, or pi/2 radians. This is the central angle. The arc length (how far the minute hand moves in 15 min) is then
s = (6 inches)(pi/2 rad) = 3pi inches, or about 9.42 inches.
25 minutes is equivalent to a central angle of (25/60)pi rad, or 1.31 radians. What is the associated arc length? Calculate this in the same way as I did for a central angle of pi/2.
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