The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Length of minute hand can be considered as radius (r) = 14 cm.

In 60 minutes the minute hand rotates 360°.

So, in 5 minutes, it will rotate = $\dfrac{360°}{60} \times 5 = 30°$.

We know that,

Area of sector of angle θ and radius r = $\dfrac{θ}{360°} \times πr^2$

Substituting values we get :

$\Rightarrow \text{Area } = \dfrac{30°}{360°} \times \dfrac{22}{7} \times 14^2 \\[1em] = \dfrac{1}{12} \times 22 \times 2 \times 14 \\[1em] = \dfrac{154}{3} \text{ cm}^2.$

Hence, the area swept by the minute hand in 5 minutes = $\dfrac{154}{3}$ cm².