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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`]
Solution
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
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