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Math Help - Volume

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    Volume

    Calculate the volume of solid 1 quadrant bounded by: x^2+y^2=4 and x^2+z^2=4


    Answer:
    \frac{16}{3}
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Calculate the volume of solid 1 quadrant bounded by: x^2+y^2=4 and x^2+z^2=4


    Answer:
    \frac{16}{3}
    V = \frac{1}{8} \int_{x = -2}^{x = 2} \int_{y = -\sqrt{4 - x^2}}^{y = + \sqrt{4 - x^2}} \int_{z = -\sqrt{4 - x^2}}^{z = +\sqrt{4 - x^2}} dz \, dy \, dx.

    Which is the same as V = \int_{x = 0}^{x = 2} \int_{y = 0}^{y = + \sqrt{4 - x^2}} \int_{z = 0}^{z = +\sqrt{4 - x^2}} dz \, dy \, dx.


    Now integrate.
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    The integral as I know build. The problem is that I do not know build the graph
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