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Math Help - word problem involving integrals

  1. #1
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    word problem involving integrals

    A bowl is in the shape of a hemisphere with a diameter 30 cm and water is poured into the bowl to a height of "h" cm. Find the volume of water in the bowl.

    Help pleeeeeease!!!!! What do I do???
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  2. #2
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    You can set up an integral using washers.

    {\pi}\int_{-15}^{h-15}(225-y^{2})dy

    Evaluate the integral and it'll give the volume at any height h.
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  3. #3
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    A few quick questions...

    Where did you get your original function from??? aka the 225 and y^2

    And why is the integral from -15 to h-15 ????

    Thanks a bunch
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  4. #4
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    The original function forms the equation for a circle, x^{2}=r^{2}-x^{2} The square of 15 is 225.

    It's -15 because if the diameter of the hemisphere is centered at the origin,the bottom would be at -15. Then, any height above that would be
    h-15.

    If you left h=15, you would get the full volume of the hemisphere.
    2250\pi
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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