Question

The minute hand of a clock is $12cm$ long, find the area of the clock described by minute hand in $42min.$

Answer 1

Angle described by the minutes hand in $60$min

$={360}^o$

Angle described, by the minutes hand in $42$ min.

$=\frac{{360}^o}{60}\times 42={252}^o$

required area swept by the minute hand in $42$ min.

$=$ Area of sector with $r=12$cm & $\theta ={252}^o$

$\therefore$ Area swept by the minutes hand in $42$min $=(\frac{\theta }{360}\times \pi r^2)$

$=\frac{252}{360}\times \frac{22}{7}\times 12\times 12$

$=\frac{36\times 22\times 12}{30}=316.8c{m}^2$.