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 $360°$.

In 5 minutes, minute hand will rotate =$\frac{ 360°}{ 60} \times 5$ = $30°$

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

Area of sector of angle $θ$ = $\frac{θ }{360°} \times π r^2$

Area of sector of $30°$= $\frac{30°}{ 360°} \times \frac{22}{ 7} \times 14 \times 14$
= $\frac{22}{ 12} \times 2 \times 14$

= $11 \times \frac{14} 3$

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

Therefore, the area swept by the minute hand in $5$ minutes is $\frac{154}3\, cm^2$.