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Thread: Mensuration

  1. #1
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    Question Mensuration

    A wire bent in the form of a circle of radius 42 cm is cut & again bent in the form of a square. How do I find the ratio of the regions enclosed by the circle & the square in the two cases?

    Thanks,

    Ron
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  2. #2
    Super Member Quacky's Avatar
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    I hope I've understood the question correctly! I'm infamous for misinterpreting what they're asking of me.

    The area of the circle initially is
    $\displaystyle \pi r^2$

    $\displaystyle =\pi42^2$

    $\displaystyle =1764\pi$

    Now, the total amount of wire is the circumference of the circle. This is $\displaystyle \pi\times d$ Where d is the diameter of the circle. As the diameter is twice the radius, $\displaystyle d=84$ and the total amount of wire is $\displaystyle 84\pi$

    Now then, one side of the square will be
    $\displaystyle \displaystyle\frac{84\pi}{4}$
    $\displaystyle =21\pi$

    The area of the square will be $\displaystyle width \times height$
    So what will the area of the square be? And then, can you finish the question?
    Last edited by Quacky; Feb 28th 2011 at 08:15 AM. Reason: Changed wording slightly
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