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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


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 85,320


Solution :
Breadth = 12 m
Length = 2 × Breadth = 2 × 12 = 24 m
Area of rectangle = Length × Breadth = 12 × 24 = 288 m2
Cost of levelling = Rs. 100 per m2
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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