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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Updated on: 10-Oct-2022

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