Question

calculator
the tip of a 7 in. minute hand of a clock sweeps out circular arcs.
what is the length of the arc made by the tip of the minute hand between 8:45 and 9:00?
use 3.14 for pi. round your answer to the nearest hundredth.
enter your answer in the box.

Explanation:

Step1: Find the central angle

From 8:45 to 9:00, the minute - hand moves 15 minutes. Since the minute - hand moves 360° in 60 minutes, the central angle \(\theta\) is \(\theta=\frac{15}{60}\times360^{\circ}=90^{\circ}\). Convert the angle to radians: \(\theta = 90^{\circ}\times\frac{\pi}{180^{\circ}}=\frac{\pi}{2}\) (using \(\pi = 3.14\), \(\theta=\frac{3.14}{2}=1.57\) radians). The radius \(r = 7\) inches.

Step2: Use the arc - length formula

The arc - length formula is \(s=r\theta\). Substitute \(r = 7\) and \(\theta=1.57\) into the formula: \(s=7\times1.57\).

Answer:

\(10.99\)