What is the area of the face of a clock described by its minute hand between 9 a.m. and 9.35 a.m; if the minute hand is 10 cm long?
(a)$36 \frac{2}{3} \mathrm{cm}^{2}$
(b)$157 \frac{1}{7} \mathrm{cm}^{2}$
(c)$183 \frac{1}{3} \mathrm{cm}^{2}$
(d)None of these
Answer
Answer (as printed): C
Explanation
Angle swept by the minute hand in 35 min $$=\left(\frac{360}{60} \times 35\right)^{\circ}=210^{\circ} .$$ ∴ Required area = Area of a sector of a circle with radius 10 cm and central angle 210° $$=\frac{\pi r^{2} \theta}{360}=\left(\frac{22}{7} \times 10 \times 10 \times \frac{210}{360}\right) \mathrm{cm}^{2}=\frac{550}{3} \mathrm{cm}^{2}=183 \frac{1}{3} \mathrm{cm}^{2} .$$