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A 4.2 m wide road surrounds a circular plot whose circumference is 176 m. Find the cost of paving the road at Rs 75 m ^{2}.

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#### Solution

Circumference of the plot = 176 m

Radius of the circuIarplot =

2πr = 176

r = `176 xx 7/22 xx 1/2`

r = 28 m

Radius of circular plot= 28 m

Area of circular plot =π r^{2}

`= 22/7 xx 28 xx 28`

= 2464 m^{2}

Area of circular plot= 2464 m^{2 }

Radius of circular plot with surrounding road= R = ( 28 + 4.2) m= 32.2 m

Area of circular plot with surrounding road = π R^{2}

`= 22/7 xx 32.2 xx 32.2`

= 3258.64 m^{2}

Area of circular plot with surrounding road =3258.64 m^{2}

Area of road =Area of circular plot with surrounding road- Area of circular plot

= (3258.64 - 2464) m^{2 }

= 794.64 m^{2}

Area of road = 794.64 m^{2}

Cost of paving one sq m = Rs. 7 5

Cost of paving the road =Rs (75 x 794.64) =Rs. 59,598

Cost of paving the road =Rs. 59,598

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