Question

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

Answer 1

In $60$ minutes, minute hand completes ${360}^0$ i.e., one rotation.

$\Rightarrow$ in $1$ minute, minute hands completes $\frac{{360}^{\circ }}{60}=6^{\circ }$

Hence, in $5$ minutes the angle covered is is $6\times 5={30}^o$.

The angle of sector formed is ${30}^o$.

The area swept by the minute hand in $5$ minutes$=\frac{30}{360}\times \pi \times 14\times 14$

Using $\pi =\frac{22}{7}$, we get

The area swept by the minute hand in $5$ minutes $=\frac{154}{3}$ sq. cm