Question

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

Hint:

For circular motion, use \( A = \frac{\theta}{360} \pi r^2 \).

Answer 1

Angle swept in 60 minutes:
\[ 360^\circ. \] Angle swept in 20 minutes:
\[ \frac{20}{60} \times 360 = 120^\circ. \] Area swept:
\[ A = \frac{\theta}{360} \pi r^2. \] \[ = \frac{120}{360} \pi (15)^2. \] \[ = \frac{1}{3} \pi \times 225. \] \[ = 75\pi. \] Approximating \( \pi = 3.14 \):
\[ = 235.5 \text{ cm}^2. \]