Question

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A path of width 3.5m runs around a semi-circular grassy plot whose perimeter is 72m.find the area of the path.(use pi=22/7)

Answer 1

Let the Radius of the Semi Circular grassy plot be : r

We know that : Perimeter of Semi Circle is given by : πr + diameter

Given : The Perimeter of Semi Circular grassy plot as : 72m

⇒ πr + diameter = 72

⇒ πr + 2r = 72

⇒ r(π + 2) = 72

⇒ $r(\frac{22}{7} + 2) = 72$

⇒ $r(\frac{36}{7}) = 72$

⇒ r = (7 × 2) = 14m

⇒ Radius of Semi Circular grassy plot is 14m

⇒ Radius of Semi Circle including the road is : (14 + 3.5) = 17.5m

From the Diagram, We can Notice that Area of the Path can be found by Subtracting the Area of Semi Circular grassy plot from the Area of Semi Circle including the Road.

We know that : Area of Semi Circle is given by :  $\frac{\pi r^2}{2}$

⇒ Area of Semi Circle including the Road :

⇒ $\frac{1}{2}(\frac{22}{7})(17.5)^2 = 11(2.5)(17.5) = 481.25\;m^2$

⇒ Area of Semi Circular grassy plot : $\frac{1}{2}(\frac{22}{7})(14)^2 = 11(2)(14) = 308\;m^2$

⇒ Area of the Path = (481.25 - 308) = 173.25 m²