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Question
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.
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 r2
`= 22/7 xx 28 xx 28`
= 2464 m2
Area of circular plot= 2464 m2
Radius of circular plot with surrounding road= R = ( 28 + 4.2) m= 32.2 m
Area of circular plot with surrounding road = π R2
`= 22/7 xx 32.2 xx 32.2`
= 3258.64 m2
Area of circular plot with surrounding road =3258.64 m2
Area of road =Area of circular plot with surrounding road- Area of circular plot
= (3258.64 - 2464) m2
= 794.64 m2
Area of road = 794.64 m2
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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