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Yakvenalex [24]
3 years ago
15

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?

Mathematics
1 answer:
Nesterboy [21]3 years ago
5 0
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.
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