Square inscribed in a circle: If the area of the circle is 220 sq m, find the area of the square inscribed in it.
Aptitude
Area
Difficulty: Medium
Choose an option
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A49
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B70
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C140
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D150
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E110
Answer
Correct Answer: 140
Explanation
Introduction / Context:This geometry problem links a circle and its inscribed square via the circle’s diameter as the square’s diagonal.
Given Data / Assumptions:
- Area of circle A_c = 220 sq m
- Inscribed square has diagonal equal to circle’s diameter (2r)
- Use π = 22/7 unless stated.
Concept / Approach:If the circle has radius r, then A_c = πr^2. For the inscribed square, diagonal d = 2r; area of square A_s = d^2 / 2 = (4r^2)/2 = 2r^2.
Step-by-Step Solution:
πr^2 = 220 → r^2 = 220 / (22/7) = 220 * 7 / 22 = 70A_s = 2r^2 = 2 * 70 = 140 sq mVerification / Alternative check:Diagonal d = 2r → area = (d^2)/2 = 2r^2, consistent with calculation above.
Why Other Options Are Wrong:49, 70, 150, 110 do not correspond to 2r^2 with r^2 = 70.
Common Pitfalls:Mistaking side for diagonal or using r instead of 2r when converting circle-to-square dimensions.
Final Answer:140