A clock has a diameter of 16 inches. How far does the hour hand travel during 5 hours? Use 3.14 for pi.
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Answer
Final Answer: The hour hand travels approximately \(\boxed{20.94}\) inches in 5 hours.
Step 1 ：The hour hand of a clock moves in a circular path. The distance it travels can be calculated using the formula for the circumference of a circle, which is \(2\pi r\), where \(r\) is the radius of the circle.
Step 2 ：In this case, the radius of the clock is half of its diameter, so \(r = \frac{16}{2} = 8\) inches.
Step 3 ：However, the hour hand only travels \(\frac{1}{12}\) of the full circle for each hour, because there are 12 hours on a clock.
Step 4 ：So, for 5 hours, the hour hand would travel \(\frac{5}{12}\) of the full circle.
Step 5 ：Calculating the circumference of the clock, we get \(2\pi r = 2\pi \times 8 = 50.26548245743669\) inches.
Step 6 ：Calculating the distance the hour hand travels in 5 hours, we get \(\frac{5}{12} \times 50.26548245743669 = 20.943951023931955\) inches.
Step 7 ：Final Answer: The hour hand travels approximately \(\boxed{20.94}\) inches in 5 hours.
