What is the area of the face of a clock described by its minutes hand between 9 am and 9 : 35 am, if the minutes hand is 10 cm long ?

Answer: Option C

Angle swept by the minute hand in 35 minutes.
$$\begin{array}{rl}& ={\left(\frac{360}{60}\times 35\right)}^{\circ }\\ & =210^{\circ }\end{array}$$
∴ Required area = Area of a sector of a circle with radius 10 cm and central angle 210°
$$\begin{array}{rl}& =\frac{\pi r^2\theta }{360}\\ & =\left(\frac{22}{7}\times 10\times 10\times \frac{210}{360}\right)\text{c}{\text{m}}^2\\ & =\frac{550}{3}\text{c}{\text{m}}^2\\ & =183\frac{1}{3}\text{c}{\text{m}}^2\end{array}$$