Question

The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :

• A. $121 \, \text{cm}^2$
• B. $131 \, \text{cm}^2$
• C. $231 \, \text{cm}^2$
• D. $172.5 \, \text{cm}^2$

Answer 1

The Correct Option is C

The area swept by the minute hand is a sector of the circle. Using the formula for the area of a sector:
\[Area = \frac{\theta}{360^\circ} \pi r^2\]
In 10 minutes, the angle swept is:
\[\theta = \frac{10}{60} \times 360 = 60^\circ\]
Substitute $r = 21 \, cm$:
\[Area = \frac{60}{360} \pi (21)^2 = \frac{1}{6} \pi \times 441 \approx 231 \, \text{cm}^2\]