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Math Help - Finding the volume of a solid(3d)

  1. #1
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    Question Finding the volume of a solid(3d)

    Problem: the solid lies between planes and perp. to the x-axis at x=-1 and x=1. the cross-sections perp. to the x-axis between these planes are squares whose base run from the semicircle y=-sqrt1-x^2 tot the semicircle y=sqrt1-x^2.

    I tried drawing this in the 3-d form, with the square cross-sections, but what would be the sides? Would it be -sqrt1-x^2 * sqrt1-x^2?
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  2. #2
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    Quote Originally Posted by hp.phoenix3 View Post
    Problem: the solid lies between planes and perp. to the x-axis at x=-1 and x=1. the cross-sections perp. to the x-axis between these planes are squares whose base run from the semicircle y=-sqrt1-x^2 tot the semicircle y=sqrt1-x^2.

    I tried drawing this in the 3-d form, with the square cross-sections, but what would be the sides? Would it be -sqrt1-x^2 * sqrt1-x^2?
    s = \sqrt{1-x^2} - (-\sqrt{1-x^2}) = 2\sqrt{1-x^2}

    V = \int_{-1}^1 (2\sqrt{1-x^2})^2 \, dx<br />
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  3. #3
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    Smile

    Quote Originally Posted by skeeter View Post
    s = \sqrt{1-x^2} - (-\sqrt{1-x^2}) = 2\sqrt{1-x^2}

    V = \int_{-1}^1 (2\sqrt{1-x^2})^2 \, dx<br />
    Thanks. I get it now.
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