A rectangular park is 100 m by 50 m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (use π = 3.14).
Answers
Answer:
The cost of levelling 9812.5 m² semicircular flower bed is ₹ 5887.50
Step-by-step explanation:
Given :
Length of a rectangular park, l = 100 m
Breadth of a rectangular park ,b = 50 m The semicircular flower beds are around the rectangular park.
Therefore, the diameters of semicircular plots with length , d1 = l
2r1 = 100
[Diameter of a circle = 2 × radius]
r1 = 100/2
r1 = 50 m
Diameters of semicircular plots with breadth , d2 = b
2r2 = 50
[Diameter of a circle = 2 × radius]
r2 = 50/2
r2 = 25 m
Total area of semicircular plot ,A = 2 × Area of semicircular plots with Length + 2 × semicircular plots with breadth
A = 2 × ½ × πr1² + 2 × ½ × πr2²
A = πr1² + πr2²
A = π(r1² + r2²)
A = 3.14 ( 50² + 25²)
A = 3.14 (2500 + 625)
A = 3.14 × 3125
A = 9812.5 m²
Cost of levelling 1 m² semicircular flower bed = ₹ 0.60
Cost of levelling 9812.5 m² semicircular flower bed = ₹ 0.60 × 9812.5 = ₹ 5887.50
Cost of levelling 9812.5 m² semicircular flower bed = ₹ 5887.50
Hence, the cost of levelling 9812.5 m² semicircular flower bed = ₹ 5887.50
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