Question

A 6m wide path is to be constructed all around and outside of a circular field of diameter 126m find cost of constructing the path at rupess 25 class 7th

Answer 1

Cost of constructing the path at rupees 25 is Rs 62172

Solution:

Given is a circular field

Diameter = 126 m

$Radius = \frac{diameter}{2}\\\\Radius = \frac{126}{2} = 63$

Thus radius is 63 m

Find area of circular field without wide path:

$Area = \pi r^2\\\\Area = 3.14 \times 63^2\\\\Area = 12462.66\ m^2$

Given that,

width of path = 6m

Radius including path = 6 + 63 = 69 m

Find area of circular field with wide path:

$Area = 3.14 \times 69^2\\\\Area = 14949.54\ m^2$

Find area of wide path

Area of path = area of circular field with wide path - area of circular field without wide path

Area of path = 14949.54 - 12462.66 = 2486.88

Find cost of constructing the path at rupees 25

$cost = 25 \times 2486.88\\\\cost = 62172$

Thus cost of constructing the path at rupees 25 is Rs 62172

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