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

Minute hand complete full circle in $1$ hour.

Angle swept by minute in $1$ hour $\left(60min\right)={360}^o$

Angle swept by minute hand in $1min=\frac{360}{60}=6^o$

Angle swept by minute hand in $5min=6\times 5={30}^o$

$\theta ={30}^o,r=14cm$

Area swept by minute hand = Area of sector

$=\frac{\theta }{360}\times \pi r^2$

$=\frac{30}{360}\times \frac{22}{7}\times (14{)}^2$

$=\frac{1}{12}\times \frac{22}{7}\times 14\times 14$

Area swept by minute hand $=\frac{154}{3}c{m}^2$