Question

suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. for the duration, determine the distance traveled by the tip of the minute hand. 30 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: Identify the path of the minute - hand

The minute - hand moves in a circular path. The radius of the circle $r = 3$ inches.

Step2: Determine the angle of rotation

In 60 minutes, the minute - hand makes a full rotation of $2\pi$ radians. In 30 minutes, the angle of rotation $\theta=\pi$ radians.

Step3: Use the arc - length formula

The formula for the arc - length $s$ of a circle is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Substitute $r = 3$ and $\theta=\pi$ into the formula: $s=3\times\pi = 3\pi$.

Answer:

$3\pi$ inches