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    Subject

    Quantitative Aptitude

    Topic

    Areas & Volumes

    Find the ratio of the areas of the incircle and circumcircle of a square.

    ক)
    1:1
    খ)
    1:2
    গ)
    1:3
    ঘ)
    1:4

    Explanation

    Let the side of the square be x. Then, its diagonal = 2x2=2x\sqrt{2x^2}=\sqrt{2x} Radius of incircle = x2\frac x2 Radius of circum circle= 2×x2=x2\sqrt2\times\frac x2=\frac x{\sqrt2} Required ratio = πx24:πx22=14:12=1:2\frac{\mathrm{πx}^2}4:\frac{\displaystyle\mathrm{πx}^2}{\displaystyle2}=\frac14:\frac12=1:2

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