Question

The minute hand of a clock is 14 cm long If it moves between 8:00 AM and 8:45 AM What is the area covered by it on the face of the clock?

• A. $512c{m}^2$
• B. $462c{m}^2$
• C. $264c{m}^2$
• D. $196c{m}^2$

Answer 1

Answer: (B)

$462c{m}^2$

The total angle in covering $1$ hour by the minute hand in a clock is ${360}^0$.
$=>60$ min $={360}^0$.
This means for $45$ minutes, angle $=\frac{{360}^0\times 45}{60}={270}^0$

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 $14$ cm and angle ${270}^0=\frac{270}{360}\times \frac{22}{7}\times 14\times 14=462{cm}^2$