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Question
A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m . Find the area of the path .
`("Use" pi= 22/7) `
Solution
Let the radius of the semicircular plot be r.
Perimeter of the semi-circular grassy plot = `pi r+2r=72`
`⇒ r=14 cm`
Given that the width of the plot = 3.5 m
Thus, the outer radius = 3.5 + 14 = 17.5 m
Area of the path = `(pi R^2)/2-(pi r^2)/2`
`= pi/2 (R^2-r^2)`
`=pi/2 ((17.5)^2-(14)^2)`
`= 173.25 m^2`
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