Question

The minute hand of a clock is $8\mathrm{cm}$ long. Find the area swept by the minute hand between$8.30\mathrm{a}.\mathrm{m}.$ and $9.05\mathrm{a}.\mathrm{m}.$

Answer 1

Find the area swept by the minute hand.

The minute hand of a clock is $8\mathrm{cm}$ long.

The area swept by the minute hand between $8:30\mathrm{a}.\mathrm{m}.$ and $9:05\mathrm{a}.\mathrm{m}.$

Angle made the center by each $5$ minutes$\frac{360}{12}=30°$.

Angle covered between $8:30\mathrm{a}.\mathrm{m}.$ to $9:05\mathrm{a}.\mathrm{m}.$ is ${210}^{\circ }$.

Therefore,

$\begin{array}{rcl}\mathrm{Area}& =& \mathrm{\pi }{\left(8\right)}^2\frac{210°}{360°}\\ & =& \frac{22}{7}\times 8\times 8\times \frac{210°}{360°}\\ & =& 117\frac{1}{3}{\mathrm{cm}}^2\end{array}$

Hence, the area is swept by the minute hand between$8:30\mathrm{a}.\mathrm{m}.$ and $9:05\mathrm{a}.\mathrm{m}.$ is $117\frac{1}{3}{\mathrm{cm}}^2$.