Question

The length of the minute hand of a clock is $21cm.$ The area swept by the minute hand in $5$ minutes is

Answer 1

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

Angle subtends by the minute hand in $1$ minute $=\frac{{360}^{\circ }}{{60}^{\circ }}=6^{\circ }$

$\therefore$ Angle subtends by the minute hand in $5$ minutes $={30}^{\circ }$

The radius of the sector made by minute hand $=$ length of minute hand $=21cm$

The angle subtended by the minute hand at the center in $5$ minutes $={60}^{\circ }$

Now, Area of the sector $=\frac{\theta }{360}\pi r^2$

Area swept by the minute hand in $5$ minute $=\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times {21}^2=115.5c{m}^2$