Question

suppose the tip of the minute hand of a clock is 4 in. from the center of the clock. for the duration, determine the distance traveled by the tip of the minute hand 6.5 hr. 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 number of full - circles

The minute - hand of a clock makes one full - circle in 1 hour. In 6.5 hours, the number of full - circles $n = 6.5$.

Step2: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle. Here, $r = 4$ inches. So, $C=2\pi\times4 = 8\pi$ inches.

Step3: Calculate the total distance

The total distance $d$ traveled by the tip of the minute - hand is the number of full - circles times the circumference of one circle. So, $d=n\times C$. Substituting $n = 6.5$ and $C = 8\pi$, we get $d=6.5\times8\pi=52\pi$ inches.

Answer:

$52\pi$ inches