Question : A rectangular lawn whose length is twice its breadth is extended by having four semi-circular portions on its sides. What is the total cost (in INR) of levelling the entire lawn at the rate of INR 100 per square metre, if the smaller side of the rectangular lawn is 12 m? (Take $\pi=3.14$)
Option 1: 85,320
Option 2: 78,650
Option 3: 86,540
Option 4: 97,625
Correct Answer: 85,320
Solution :
Breadth = 12 m
Length = 2 × Breadth = 2 × 12 = 24 m
Area of rectangle = Length × Breadth = 12 × 24 = 288 m
2
Cost of levelling = Rs. 100 per m
2
Area of semi-circle = $\frac{1}{2}$ × $\pi r^2$
Area of semi-circle on larger side = $\frac{1}{2} \times \pi \times 12^2$ = $72\pi$ m$^2$
Area of semi-circle on smaller side = $\frac{1}{2} × \pi × 6^2$ = $18\pi$ m$^2$
The total area of the lawn = Area of the rectangle + 2 × Area of the semi-circle on the larger side + 2 × Area of the semicircle on the smaller side
Total area of lawn = 288 + (2 × 72$\pi$ ) + (2 × 18$\pi$)
Total area of lawn = 288 + 2$\pi$(72 + 18) = 288 + 2 × 3.14 × 90
= 288 + 565.2 = 853.2 m$^2$
The total cost of levelling = Total area of lawn × 100
= 853.2 × 100
= 85,320
Hence, the correct answer is INR 85,320.
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