Question

suppose the tip of the minute hand of a clock is 12 in. from the center of the clock. for the duration, determine the distance traveled by the tip of the minute hand 50 min the distance traveled by the tip of the minute hand is (simplify your answer. type your answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find the angle covered

The minute - hand of a clock covers a full - circle ($360^{\circ}$ or $2\pi$ radians) in 60 minutes. In 50 minutes, the angle $\theta$ covered is $\theta=\frac{50}{60}\times2\pi=\frac{5\pi}{3}$ radians.

Step2: Use the arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Given $r = 12$ inches and $\theta=\frac{5\pi}{3}$, then $s=12\times\frac{5\pi}{3}$.

Step3: Simplify the expression

$12\times\frac{5\pi}{3}=\frac{12\times5\pi}{3}=20\pi$ inches.

Answer:

$20\pi$ inches