What is the area of the circular field?

Statement I: The area of the largest square that can be inscribed in the given circular field is 6400 sq. cm.

Statement II : The area of the smallest square in which the given circular field can be inscribed is 4900 sq. cm.

From statement I: Diagonal of the square = Diameter of the circular field Side of square = √6400 cm = 80 cm diagonal of square = √2 side = √2 × 80 = 80√2 cm So 80√2 = 2r So r = 80/√2 Hence Area of the circular field = πr^{2} = π×(80/√2)^{2} = π×6400/2= 3200π cm^{2} From statement II: Side of a square = √4900 = 70 cm = diameter of circle So 2r = 70 or r = 35cm Area of circular field = πr^{2} = π×35^{2} = 1225π cm^{2} So answer can be determined by either of statement I or II.

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