Question

The minute hand of a clock is 15 cm long. Calculate the area swept by it in 20 minutes.

Answer 1

Angle inscribed by the minute hand in 60 minutes = ${360}^{\circ }$
Angle inscribed by the minute hand in 20 minutes = $\frac{360}{60}\times 20={120}^{\circ }$

We have:
$\theta ={120}^{\circ }\mathrm{and}r=15\mathrm{cm}$

∴ Required area swept by the minute hand in 20 minutes = Area of the sector with r = 15 cm and $\theta ={120}^{\circ }$
$=\frac{{\mathrm{\pi r}}^2\mathrm{\theta }}{360}$

$$\begin{gathered} =3.14\times 15\times 15\times \frac{120}{360} \\ =235.5{\mathrm{cm}}^2 \end{gathered}$$