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A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Given:
A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path.
To do:
We have to find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Solution:
Let the radius of the circular pond be $r$ and the width of the path be $w$.
This implies,
Radius of the outer circle $R=r+w$
$R=\frac{17.5}{2}+2$
$R=8.75+2$
$R=10.75\ m$
Area of the path $=$ Area of the outer circle $-$ Area of the pond
$=\pi (10.75)^2-\pi (8.75)^2$
$=3.14(115.5625-76.5625)$
$=3.14\times39$
$=122.46\ m^2$
Rate of construction $=Rs.\ 25$ per $m^2$
The cost of constructing the path $=Rs.\ 25\times 122.46$
$=Rs.\ 3061.50$
The cost of constructing the path is Rs. 3061.50.
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