Question

How far does the tip of the minute hand of a clock move in 25 minutes if the hand is 9 inches long?

Answer 1

so let's recall that a circle, has a total of 360°, so the circular clock has a total of 360°, and it also has 60 minutes, so, how many degrees for 1 minute? 360/60 = 6. So there are 6° in 1 minute, then in 25 minutes the minute hand has travelled 25 * 6 degrees, namely 150°, and that' the central angle for 25 minutes then. Since the hand is 9 inches long, that'd be the radius.

`\bf \textit{arc's length}\\\\ s=\cfrac{r\pi \theta }{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=9\\ \theta =150 \end{cases}\implies s=\cfrac{(9)(\pi )(150)}{180}\implies s=\cfrac{15\pi }{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 23.56194490192344928847~\hfill`