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    The area of the greatest circle that can be inscribed inside a square of side 21 cm is:
    Question

    The area of the greatest circle that can be inscribed inside a square of side 21 cm is:

    A.

    347 cm2\text{cm}^2​​

    B.

    351.5 cm2\text{cm}^2

    C.

    346.5 cm2\text{cm}^2

    D.

    350.5 cm2\text{cm}^2

    Correct option is C

    Given:

    Side of the square = 21 cm

    Formula Used:
    Area of a circle is given by:

    Area = πr2 \pi r^2

    Solution:

    A circle is inscribed, so its diameter = side of the square
    Radius =212= \frac{21}{2} =​ 10.5 cm

    Area =227×(10.5)2 \frac{22}{7} \times (10.5)^2

    =227×110.25=346.5 cm2 \frac{22}{7} \times 110.25 = 346.5 \text{ cm}^2

    The area of the greatest inscribed circle is 346.5 cm²

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