Question

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

Answer 1

We know that in 1 hour (i.e., 60 minutes), the minute hand rotates \(360°\).

In 5 minutes, minute hand will rotate =\(\frac{ 360°}{ 60} \times 5\) = \(30°\)

Therefore, the area swept by the minute hand in 5 minutes will be the area of a sector of \(30°\) in a circle of \(14 \,cm\) radius.

Area of sector of angle \(θ\) = \(\frac{θ }{360°} \times π r^2\)

 Area of sector of \(30°\)= \(\frac{30°}{ 360°} \times \frac{22}{ 7} \times 14 \times 14\)
 = \(\frac{22}{ 12} \times 2 \times 14\)

 = \(11 \times \frac{14} 3\)

 = \(\frac{154}3 \,cm^2\)

Therefore, the area swept by the minute hand in \(5\) minutes is \(\frac{154}3\, cm^2\).