Question

- A7m wide path is to be constructed all around, and outside of a circular field of diameter 112 m
Find the cost of constructing the path at 50.​

Answer 1

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196350 Rs. Sqr. m is the cost of constructing the path at 75 Rs per sq m.

Step-by-step explanation:

The diameter of garden = 112m

So, the Radius of garden (r) = 112m/2

                                         = 56m

Now, The Radius of Outer circle made by path constructed (R) = 56m + 7m

                                                                                                   = 63m

        The Area of garden = pi * r * r

                                          = 22/7 * 56m * 56m

                                          = 9856 sqr. m

       The Area of garden including path = pi * R * R

                                         = 22/7 * 63m * 63m

                                         = 12474 sqr. m

Now,

The Area of Path Constructed = Area of garden including path - Area of  garden

                                                  = 12474 sqr. m - 9856 sqr. m

                                                  = 2618 sqr m

Now,

        Rate of construction of 1 sqr m path = 75 Rs

        Cost of Construction of 2618 sqr m = 75 Rs. * 2618 sqr m

                                                                      = 196350 Rs

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Answer 2

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196350 Rs. Sqr. m is the cost of constructing the path at 75 Rs per sqm.

Step-by-step explanation:

The diameter of garden = 112m

So, the Radius of garden (r) = 112m/2

                                         = 56m

Now, The Radius of Outer circle made by path constructed (R) = 56m + 7m

                                                                                                   = 63m

The Area of garden = pi * r * r

                              = 22/7 * 56m * 56m

                                        = 9856 sqr.m

       The Area of garden including path = pi * R * R

                             = 22/7 * 63m * 63m

                             = 12474 sqr.

Now,

The Area of Path Constructed = Area of garden including path - Area of  garden

              = 12474 sqr. m - 9856 sqr. m

               = 2618 sqr m

Now,

Rate of construction of 1 sqr m path = 75 Rs

  Cost of Construction of 2618 sqr m = 75 Rs. * 2618 sqr m

                                                                 =Rs 196350

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