The area of a circle is 220 sq m.\nA square is inscribed in this circle (all 4 vertices of the square lie on the circle).\nWhat will be the area of the inscribed square in sq m?

Introduction:
This question tests the relationship between a circle and an inscribed square. When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Using this key geometric fact, we can connect the given area of the circle to the area of the square. The problem is not about guessing values; it is about converting circle area into radius, then using the diagonal-to-side relationship of a square to compute the square’s area. This also checks whether you can move between area formulas and Pythagoras-style relationships without using any advanced geometry.

Given Data / Assumptions:

• Area of circle = 220 sq m
• Circle area formula: A = pi * r^2
• For an inscribed square: diagonal of square = diameter of circle = 2r
• For a square: diagonal = side * sqrt(2)

Concept / Approach:
First find r^2 from the circle area. Then use the inscribed-square relation: side = (2r)/sqrt(2) = r*sqrt(2). Finally, square area = side^2 = (r*sqrt(2))^2 = 2*r^2. This avoids unnecessary steps and directly links square area to r^2.

Step-by-Step Solution:
pi * r^2 = 220r^2 = 220 / piArea of inscribed square = 2 * r^2So square area = 2 * (220 / pi) = 440 / piUsing pi = 22/7: square area = 440 * (7/22) = 140

Verification / Alternative Check:
Since the square’s diagonal is the circle’s diameter, the square is “as large as possible” inside the circle. That means its area must be a fixed fraction of the circle’s r^2 value. The derived relation square area = 2*r^2 is standard and confirms consistency. Plugging r^2 = 220/pi gives 440/pi, and with pi = 22/7 it becomes exactly 140, matching one option cleanly.

Why Other Options Are Wrong:
150 sq m: would require a slightly larger r^2 than given by the circle area.70 sq m: is half of the correct value, usually from missing the factor 2.49 sq m: unrelated to the geometry; typically a random guess.110 sq m: comes from incorrect diagonal-side conversion.

Common Pitfalls:
Assuming square side equals circle radius (incorrect).Forgetting diagonal of square equals diameter of circle, not radius.Not squaring correctly when converting side to area.Mixing up pi approximations inconsistently.

Final Answer:
140 sq m