Question

The minute hand of a clock is $\sqrt{21}$ cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Answer 1

There are 12 divisions on a clock face.

So when the minute needle rotates around its pivot, it subscribes a complete angle that is

${360}^{\circ }$

So each division of the clock face corresponds to $\frac{{360}^{\circ }}{12}$= ${30}^{\circ }$

So now using the sector formula we have

Area of the sector= = $\frac{\theta }{360}$ x( $\pi$ x $r^2)$

= $\frac{{30}^{\circ }}{{360}^{\circ }}$ . $\frac{22}{7}.\sqrt{21}$. $\sqrt{21}$

=$\frac{11}{2}$

= 5.5 ${cm}^2$