A circular pond is \[17.5\] m is of diameter. It is surrounded by a \[2\] m wide path. Find the cost of constructing the path at the rate of Rs \[25\] per \[{{m}^{2}}\]

Home » A circular pond is m is of diameter. It is surrounded by a m wide path. Find the cost of constructing the path at the rate of Rs per

A circular pond is

$17.5$

m is of diameter. It is surrounded by a

$2$

m wide path. Find the cost of constructing the path at the rate of Rs

$25$

per

${{m}^{2}}$

A circular pond is

$17.5$

m is of diameter. It is surrounded by a

$2$

m wide path. Find the cost of constructing the path at the rate of Rs

$25$

per

${{m}^{2}}$

Solution:

Given Diameter of the circular pond =

$17.5$

m

Let us consider r be the radius of the park =

$(17.5/2)$

m =

$8.75$

m

Given The circular pond is surrounded by a path of width

$2$

m.

So, Radius of the outer circle = R =

$(8.75+2)$

m =

$10.75$

m

We know that Area of the road = Area of the outer circular path – Area of the circular pond

=

$\pi {{r}^{2}}-\pi {{R}^{2}}$

=

$3.14\times {{(10.75)}^{2}}-3.14\times {{(8.75)}^{2}}$

=

$3.14\times ({{(10.75)}^{2}}-{{(8.75)}^{2}})$

=

$3.14\times ((10.75+8.75)\times (10.75-8.75))$

=

$3.14\times 19.5\times 2$

=

$122.46$

m²

Hence, the area of the path is 122.46

${{m}^{2}}$

Now, given Cost of constructing the path per

${{m}^{2}}$

= Rs. 25

So, cost for constructing

$122.46$

${{m}^{2}}$

of the path = Rs.

$25\times 122.46$

= Rs.

$3061.50$

i

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