Ravi cuts a square field of maximum possible area from his circular field.…
2025
Ravi cuts a square field of maximum possible area from his circular field. Find the area of the remaining circular field if the cost of grass cutting of the square field at Rs. 4 per m2 is Rs. 882 ?
- A.
120 m2
- B.
126 m2
- C.
121 m2
- D.
116 m2
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Correct Option
Option B: 126 m²
Step-by-Step Solution
Calculate the area of the square field:
Given the cost of grass cutting is Rs. 882 at a rate of Rs. 4 per m².
Area of square = 882 / 4 = 220.5 m².
Find the dimensions of the square:
Since the area of a square is side², side² = 220.5.
The diagonal of the inscribed square equals the diameter (d) of the circle.
Diagonal of a square = side * sqrt(2). Therefore, diagonal² = side² * 2 = 220.5 * 2 = 441.
Diameter (d) = sqrt(441) = 21 m.
Calculate the area of the circular field:
Radius (r) = d / 2 = 21 / 2 = 10.5 m.
Area of circle = (22/7) * r * r = (22/7) * 10.5 * 10.5 = 346.5 m².
Calculate the remaining area:
Remaining area = Area of circle - Area of square.
Remaining area = 346.5 - 220.5 = 126 m².