A circular pond is of diameter `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 square metre.

Explanation

Given that, a circular pond is surrounded by a wide path.
The diameter of circular pond = `17.5`m
`:.` Radius of circular pond `(r _(i))= ("Diameter")/(2)`
i.e., `OA = r_(i) = (17.5)/(2) = 8.75m`
and the width of the path = 2m
i.e., AB = 2m
Now, length of `OB=OA + AB = r_(i)+ AB`
Let `(r_(e)) = 8.75 + 2 = 10.75 m`
So, area of circular path = Area of outer circle i.e., (circular pond + path) - Area of circular pond
= `pir_(e)^(2) - pir_(i)^(2)` [ `because` area of circle = `pir^(2)`]
= `pi(r_(e)^(2) -r_(i)^(2))`
= `pi{(10.75)^(2) - (8.75)^(2)}`
= `pi{(10.75 + 8.75)(10.75 - 8.75)}`
= `3.14 xx 19.5xx2`
= `122.46 m^(2)`
Now, cost of constructing the path per square metre = Rs. 25
`:.` Cost constructing the path `Rs. 122.46 m^(2) = 122.46xx25`
= Rs. `3061.50`
Hence, required cost of constructing the path at the rate of Rs. 25 per `m^(2)` is Rs. `3061.50`.