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Math Help - 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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    Windsor, South-East England
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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
    \pi r^2

    =\pi42^2

    =1764\pi

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

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

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