A circular pond is of 17.5 m in diameter.It is surrounded by a 2 m wide path.Find the cost of constructing the path at the rate of Rs. 25 per m².
Answers
outer circle radius= (17.5/2)+2=10.75m
outer circle area= pi*r2=3.14*(10.75)2
=3.14*115.5625
=362.86625 m2
inner circle radius= 17.5/2=8.75m
inner circle area=pi*r2=3.14*(8.75)2
=240.40625 m2
Area of the path= 362.86625-240.40625
=122.46 m2
cost of constructing it= 25*122.46
=Rs 3061.5
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Given Data:
Diameter of the Pond ,d = 17.5 mDiameter of the Pond including 2m path ,D = 17.5m + 2m = 19.5m
Diameter of the Pond including 2m path ,D = 17.5m + 2m = 19.5m
Cost of construction per m² = 25 ₹ /m²
Formulaes :
Area of the Circle = πr²
Method of Simplification:
1) Total cost of construction = [Total area of the Circular Path × Cost per metre square.]
2) Total area of the constructed path = [Area of larger circle including Pond and path - Area of smaller circle including only Pond.]
Substitution and Simplification:
Total area of circular path ,A = π(r2)² - π(r1)²
=> A = π [ (r2)² - (r1)² ]
=> A = 3.14 × [ 115.5625 - 76.5625]
=> A = 3.14 × 39
=> A = 122.46 m²
Therefore,
Total cost of construction = 122.46 × 25 = ₹3061.5
Hence ,Total cost of construction of circular path around the Pond is ₹3061.5
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