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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 \[{{m}^{2}}\]
Areas Related to Circles | Exercise 11.4 | Maths | NCERT Exemplar
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. \[3061.50\]

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