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 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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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 area (in ${m}^2$ ) of the lawn if the smaller side of the rectangle is 12 m? (Take $\pi=3.14$ )
Option 1: 853.2
Option 2: 308.64
Option 3: 444
Option 4: 548.32
Question : The sides of a triangular park are 35 m, 53 m, and 66 m. The cost of levelling the park at the rate of INR 9.25 per m2 is:
Option 1: INR 8,584
Option 2: INR 8,547
Option 3: INR 8,621
Option 4: INR 8,510
Question : The sides of a triangular park are 60 m, 112 m and 164 m. The cost of levelling the park at the rate of INR 8.50/m2 is:
Option 1: INR 18,164
Option 2: INR 17,085
Option 3: INR 17,136
Option 4: INR 18,316
Question : The sides of a triangular field are 120 m, 170 m and 250 m. The cost of levelling the field at the rate of INR 7.40/m2 is:
Option 1: INR 65,120
Option 2: INR 63,640
Option 3: INR 59,200
Option 4: INR 66,600
Question : The internal length of a room is two times its breadth and three times its height. The total cost of painting its four walls at the rate of INR 25/m2 is INR 3,600. What is the cost of laying a carpet on its floor at the rate of INR 90.50/m2?
Option 1: INR 6,516
Option 2: INR 7,240
Option 3: INR 5,430
Option 4: INR 5,970
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