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Question

In each of the following questions, a question is followed by two statement. Read all the statements and find that which statements are required to answer the question and answer accordingly.

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.

A If the data in statement I alone is sufficient to answer the question. Correct Answer Incorrect Answer
B If the data in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
C If the data either in statement I alone or statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
D If the data given in both I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
E If the data in both the statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

Solution

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 = πr2 = π×(80/√2)^2 = π×6400/2= 3200π cm2 From statement II: Side of a square = √4900 = 70 cm = diameter of circle So 2r = 70 or r = 35cm Area of circular field = πr2 = π×352 = 1225π cm2 So answer can be determined by either of statement I or II.

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