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Math Help - Volume of cone with variable height

  1. #1
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    Volume of cone with variable height

    I haven't really done much with volumes in the past, and this question is driving me insane.

    A container is in the shape of an inverted cone of height 80cm and diameter 40 cm.

    Find the volume, Vcm^3, of water in the container when the depth is x cm.

    Thanks heaps for your help!
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  2. #2
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    Quote Originally Posted by freswood
    I haven't really done much with volumes in the past, and this question is driving me insane.

    A container is in the shape of an inverted cone of height 80cm and diameter 40 cm.

    Find the volume, Vcm^3, of water in the container when the depth is x cm.

    Thanks heaps for your help!
    The volume of a cone is,
    V=\frac{1}{3}\pi r^2h

    When the depth is x what is its radius at that time? Below is the picture of the section of the cone, note the similar triangles.
    Thus,
    \frac{20}{r}=\frac{80}{x}
    Thus,
    r=x/4
    Thus,
    V=\frac{1}{3}\pi(x/4)^2x^2=\frac{1}{48}\pi x^3
    Attached Thumbnails Attached Thumbnails Volume of cone with variable height-picture3.gif  
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  3. #3
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    Thanks so much! Are you a mathematician, or just an enthusiast?
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  4. #4
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    Quote Originally Posted by freswood
    Thanks so much! Are you amathematician
    A mathematician is not a profession one may earn. As in, a scientist, physicist, engineer, doctor. Rather, it is a title given as a gift by humanity acknowledging his accomplishments which given him immortality.
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