Question

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.  [Use `pi = 22/7`]

Answer 1

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

In 5 minutes, minute hand will rotate = `360^@/60xx5 = 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 = `θ/(360°) xx pir^2`

Area of sector of 30° =`(30°)/(360°)xx22/7xx14xx14`

`=22/12xx2xx14`

`=(11xx14)/3`

=`154/3` cm²

Therefore, the area swept by the minute hand in 5 minutes is `154/3` cm²