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

We know that in 1 hour (i.e., 60 minutes), the minute hand rotates${360}^{\circ }$

In 5 minutes, minute hand will rotate = $\frac{360}{60}$. 5 = ${30}^{\circ }$ =

Therefore, the area swept by the minute hand in 5 minutes will be the area of a sector of ${30}^{\circ }$ in a circle of 14 cm radius.

Area of sector of angle θ = $\frac{\theta }{{360}^{\circ }}$ . $\pi$. $r^2$

Area of sector of 30° = $\frac{{30}^{\circ }}{{360}^{\circ }}$ $\frac{22}{7}$ . 14 .14

$\to$ = $\frac{22}{12}$ . 2 .14
= $\frac{\left(11\right).\left(14\right)}{3}$

= $\frac{154}{3}{cm}^2$

= 51.33 ${cm}^2$

Therefore, the area swept by the minute hand in 5 minutes is 51.33 ${cm}^2$