Question

The minute hand of a clock is 7 cm long Find the area traced out by the minute hand of the clock between 6 pm to 6:30 pm

• A. $14.4c{m}^2$
• B. $15.4c{m}^2$
• C. $7.2c{m}^2$
• D. $6.42c{m}^2$

Answer 1

The correct option is D $6.42c{m}^2$

The total angle of $12$ hours in a clock is
${360}^0$.
$=>24$ half hours $={360}^0$.
This means for one half an hour, angle $=\frac{{360}^0}{24}={15}^0$

Area of a sector of a circle of radius 'r' and angle
$\theta =\frac{\theta }{360}\pi r^2$
Hence, area of the sector of the circle of radius $7$ cm and angle ${15}^0=\frac{15}{360}\times \frac{22}{7}\times 7\times 7=6.42{cm}^2$