The minute hand of a clock is 6 inches long and moves from 3 o'clock to 5 o'clock. How far does the tip of the minute hand move? Express your answer rounded to two decimal places.
Answer (2)
f ro m 3 o ′ c l oc k t o 5 o ′ c l oc k i s 2 h o u rs 12 h o u rs → 36 0 0 2 h o u rs → α α = 12 2 ⋅ 36 0 0 = 6 0 0 x = 36 0 0 6 0 0 ⋅ 2 π ⋅ 6 [ in ] = 6 1 ⋅ 12 π [ in ] = 2 π [ in ] ≈ 2 ⋅ 3.14 [ in ] = 6.28 [ in ]
The tip of the minute hand moves approximately 6.28 inches when it goes from 3 o'clock to 5 o'clock. This is calculated by determining the angle the hand moves and using the arc length formula. The calculations show that the movement corresponds to a 60 degree turn, resulting in an arc length of 2π inches or about 6.28 inches.
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