Question

suppose the tip of the minute hand of a clock is 2 in. from the center of the clock. for the duration, determine the distance traveled by the tip of the minute hand. 4.5 hr

Explanation:

Step1: Determine revolutions in 4.5 hours

The minute hand makes 1 revolution per hour. So in 4.5 hours, it makes \( 4.5 \) revolutions.

Step2: Find circumference of the circle

The radius \( r = 2 \) in. The formula for circumference \( C = 2\pi r \). Substituting \( r = 2 \), we get \( C = 2\pi(2)=4\pi \) inches.

Step3: Calculate total distance traveled

Total distance is number of revolutions times circumference. So distance \( d = 4.5\times4\pi \). \( 4.5 = \frac{9}{2} \), so \( d=\frac{9}{2}\times4\pi = 18\pi \approx 56.55 \) inches.

Answer:

The distance traveled is \( 18\pi \) inches (or approximately \( 56.55 \) inches).