Question

The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Answer 1

Angle described by the minute hand in 60 minutes$=360°$
Angle described by the minute hand in 35 minutes$=\left(\frac{360}{60}\times 35\right)°$
$=210°$
Now,
$r=12\mathrm{cm}\mathrm{and}\mathrm{\theta }=210°$
∴ Required area described by the minute hand in 35 minutes = Area of the sector where $r=12\mathrm{cm}\mathrm{and}\mathrm{\theta }=210°$
$$\begin{gathered} =\frac{{\mathrm{\pi r}}^2\mathrm{\theta }}{360} \\ =\left(\frac{22}{7}\times 12\times 12\times \frac{210}{360}\right){\mathrm{cm}}^2 \\ =264{\mathrm{cm}}^2 \end{gathered}$$