The minute hand of a clock is 7 cm long. What area does it sweep in 10 minutes? Take $\pi=\dfrac{22}{7}$.

In 60 minutes the hand sweeps $360^\circ$, so in 10 minutes it sweeps $60^\circ$. The swept region is a sector of radius 7 cm, so its area is $\dfrac{\pi r^2\theta}{360}=\dfrac{22}{7}\cdot\dfrac{7\cdot 7\cdot 60}{360}=\dfrac{77}{3}\approx 25.67$ sq cm. A common mistake is to use $6^\circ$ instead of $60^\circ$, which is the angle per minute, not for 10 minutes.