A circular pond has a diameter of 17.5 , m. I | vedclass

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(D) Given that,a circular pond is surrounded by a path of width $2 \, m$.Diameter of the circular pond $= 17.5 \, m$.Radius of the circular pond $(r_i

Vedclass · Accepted Answer

$3061.50$

Vedclass · Answer

(D) Given that,a circular pond is surrounded by a path of width $2 \, m$.Diameter of the circular pond $= 17.5 \, m$.Radius of the circular pond $(r_i) = \frac{17.5}{2} = 8.75 \, m$.Width of the path $= 2 \, m$.Radius of the outer circle including the path $(r_e) = 8.75 + 2 = 10.75 \, m$.Area of the circular path $= \pi r_e^2 - \pi r_i^2 = \pi(r_e^2 - r_i^2) = \pi(r_e + r_i)(r_e - r_i)$.Area $= \frac{22}{7} 	imes (10.75 + 8.75) 	imes (10.75 - 8.75) = \frac{22}{7} 	imes 19.5 	imes 2$.Area $= \frac{22 	imes 39}{7} \approx 122.57 \, m^2$.Using $\pi \approx 3.14$,Area $= 3.14 	imes 19.5 	imes 2 = 122.46 \, m^2$.Cost of constructing the path $= 	ext{Area} 	imes 	ext{Rate} = 122.46 	imes 25 = Rs. \, 3061.50$.

$A$ circular pond has a diameter of $17.5 \, m$. It is surrounded by a $2 \, m$ wide path. Find the cost of constructing the path at the rate of $Rs. \, 25$ per $m^2$ (in $Rs.$).

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