Question

Find the area of the sector in a clock swept by the minute hand in five minutes if the radius is 14 cm.

$\left(Take\pi as\frac{22}{7}\right)$

• A. $616c{m}^2$
• B. $51.33c{m}^2$
• C. $42c{m}^2$
• D. None of the above

Answer 1

The correct option is B $51.33c{m}^2$

Area of sector
$=\frac{\theta }{360}\times \pi r^2$

To find the area of the sector, we need the angle of the sector, denoted by θ in the figure.

Now, In 60 minutes, the minute hand sweeps an angle of
${360}^{\circ }$

Hence, in 5 minutes, the angle swept would be given by
$\frac{\theta }{360}=\frac{5}{60}$

Thus,
$\theta ={30}^{\circ }$

Area of the sector

$=\frac{\theta }{360}\times \pi r^2=\frac{30}{360}\times \frac{22}{7}\times {14}^2$

$=51.33c{m}^2$