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    Subject

    Quantitative Aptitude

    Topic

    Mensuration

    The difference between the circumference and the radius of a circle is 111 cm. The area of the circle is

    ক)
    1346 cm2
    খ)
    1300 cm2
    গ)
    1386 cm2
    ঘ)
    1400 cm2
    ঙ)
    None of these

    Explanation

    We know that, circumference of circle = 2πr Where r = radius of circle As per information given in problem, ∴ 2πr – r = 111 ⇒ r (2π – 1) = 111 ⇒  r  =  1112π−1  ⇒  r  =  1112  ×  227  −  1  =  111  447  −  1  ⇒  r  =  111×  7    37  \begin{array}{l} \Rightarrow \;r\; = \;\frac{{111}}{{2\pi - 1\;}}\\ \Rightarrow \;r\; = \;\frac{{111}}{{2\; \times \;\frac{{22}}{7}\; - \;1\;}} = \;\frac{{111}}{{\;\frac{{44}}{7}\; - \;1\;}}\\ \Rightarrow \;r\; = \;\frac{{111 \times \;7\;}}{{\;37\;}} \end{array} ⇒ r = 21 cm Now, area of circle, A = πr 2 ∴A = (22/7) × 21 × 21 ⇒ A = 1386 cm 2

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