Question

The length of the minute hand of a clock is 14 cm. What is the area swept by the minute hand in 5 minutes?

• A. $\frac{160}{3}c{m}^2$
• B. $\frac{154}{3}c{m}^2$
• C. $\frac{150}{3}c{m}^2$
• D. $\frac{164}{3}c{m}^2$

Answer 1

The correct option is B $\frac{154}{3}c{m}^2$

Here, minute hand of clock acts as radius of the circle.
$\therefore$ Radius of the circle (r) = 14 cm
Angle rotated by minute hand in 1 hour $={360}^{\circ }$
$\therefore$ Angle rotated by minute hand in 5 minutes $={360}^{\circ }\times \frac{5}{60}={30}^{\circ }$
Area of the sector making angle $\theta$
$=\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi r^2$
Area of the sector making angle ${30}^{\circ }$
$=\left(\frac{{30}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$
$=\left(\frac{1}{12}\right)\times {14}^2\pi =\frac{196}{12}\pi c{m}^2=\left(\frac{49}{3}\right)\times \left(\frac{22}{7}\right)c{m}^2=\frac{154}{3}c{m}^2$
Hence, the area swept by the minute hand in 5 minutes
$=\frac{154}{3}c{m}^2$