Question

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.

Part 1: How many radians does the minute hand move from 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?

Answer 1

part1

there are 360° in a circle (clock), and thus if we check how many degrees in a clock with 60minutes, then it'd be 360/60, or 6° per minute

now, the clock went from 3:35 to 3:55, 20 minutes, how many degree is that? 6*20

part2

$\bf \textit{length of an arc}\\\\ s=\cfrac{r\theta\pi }{180}\qquad \begin{cases} r=radius\\ \theta=\textit{angle in degrees}\\ ----------\\ r=4\\ \theta=6\cdot 20 \end{cases}\implies s=\cfrac{4\cdot 6\cdot 20\cdot \pi }{180}$