Question

    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. Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer –
    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 = 40√2 Hence Area of the circular field = πr2 = π×(40√2)^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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