Question

The length of a minute hand of a clock is $12cm$. How much area will it cover on the circular dial in an interval of $5$ minutes? How much area remains to complete the revolution? $(\pi =3.14)$

Answer 1

The clock will move in circular motion. The radius if the circle is $12$cm.

circumference$=2\pi r$

$=2\times \frac{22}{7}\times 12=\frac{44\times 12}{7}=\frac{528}{7}cm=75.428cm$

Distance covered in $5$ minutes

$=\frac{360}{60}\times 5={30}^{\circ }$

Distance covered in $1^{\circ }=\frac{75.728}{{360}^{\circ }}=0.209$

Distance covered in ${30}^{\circ }$

$=0.209\times 30=6.27cm$

Area minute hand will cover on the circular dial in interval if minute is $6.27{cm}^2$

Area left$=(75.428-6.27){cm}^2=69.158{cm}^2$