Question

the minute hand on a clock is 6 inches long. between 1:15 p.m. and 1:40 p.m., the minute hand travels along an arc subtended by an angle of 150°. approximately how many inches does the tip of the minute hand travel along the arc during that time?
a. 7.85 inches
b. 47.12 inches
c. 15.71 inches
d. 21.99 inches

Explanation:

Step1: Recall Arc Length Formula

The formula for the length of an arc is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians. First, convert \( 150^\circ \) to radians. We know that \( \theta_{radians} = \theta_{degrees} \times \frac{\pi}{180} \), so \( 150^\circ \times \frac{\pi}{180} = \frac{5\pi}{6} \) radians.

Step2: Identify Radius and Calculate Arc Length

The radius \( r \) of the minute hand is 6 inches. Substitute \( r = 6 \) and \( \theta = \frac{5\pi}{6} \) into the arc length formula: \( s = 6 \times \frac{5\pi}{6} = 5\pi \approx 5 \times 3.1416 = 15.708 \approx 15.71 \) inches.

Answer:

C. 15.71 inches