Question

How far does the tip of the minute hand of a clock move in 1 hour and 27 minutes if the hand is 2 inches long?

Answer 1

so, a full circle has 360°, thus when the minute hand does one hour, it does a full circle, therefore 360°.

now, how many degrees are there in 1 minute? well, there are 60 minutes in 360°, therefore there are 360/60 degrees in 1 minute, or 6°.

now, we know in 1 hour there are 360°, how many in 27 minutes? well, 27 * 6, or 162°. So after 1hr and 27min, the minute hand has done 360+162 or 522°.

we also know the minute hand is 2 inches long, thus


`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=2\\ \theta =522 \end{cases}\implies s=\cfrac{\pi \cdot 522\cdot 2}{180}`


which is roughly 18 inches rounded up.