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Math Help - Can't figure out how a area forumla was derived for a Slicing Method problem

  1. #1
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    Can't figure out how a area forumla was derived for a Slicing Method problem

    Hi, new poster here, so please forgive any mistakes of mine.
    I've been trying to solve this problem : "The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares."
    in an effort to study for an upcoming test I have.

    My problem comes down to finding A(x) which I figured would be an area of a square, who's side length is equal to the formula for a semi circle or B - \sqrt{r^2 - (x - A)^2}, which ends up to be \sqrt{25 - x^2} right if the semi circle is centered on (0,0)? Well I went to check to see and the answer they had was 2\sqrt{25-x^2}.

    The question is, where the heck did that 2 come from? Because for the life of me I can't reason where it came from.

    Thanks in advance for any help
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  2. #2
    MHF Contributor
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    You must get a better relationship with symmetry.

    Integation is on [-5,5] as you have it.

    Due to symmetry, this is equivalent to twice the value of integration on [0,5] still using hte argument as you have it.
    Last edited by TKHunny; May 17th 2011 at 07:05 PM. Reason: Fix limits
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