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The minute hand of a clock is 9 cm long…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The minute hand of a clock is $9$ cm long. How far does its tip move between 2:10 and 2:45? What area does the hand sweep over in that time?

Need a reminder? The key ideaShow

With $\theta$ in radians, an arc is $s = r\theta$ and a sector has the area $A = \frac{1}{2}r^2\theta = \frac{1}{2}rs$ . A rolling wheel moves $2\pi r$ in each turn. For $n$ revolutions each minute, $\omega = \frac{2\pi n}{60}$ rad/s, and a point on the rim moves at $v = r\omega$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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