Square inscribed in a circle: If the area of the circle is 220 sq m, find the area of the square inscribed in it.

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:

Verification / 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