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Math Help - Find Volume of Solid S

  1. #1
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    Find Volume of Solid S

    Find the volume V of the described solid S. A pyramid with height 3h and a rectangular base with dimensions 3b and 6b.

    So I found the following: 3b[1-y/3h) and 6b(1-y/3h) --> Which I belive is where the error is coming from because I cant seem to get the correct answer.

    Integral from a=0,b=h of 18h^2(1-y/3h)^2 dy

    = from 0 to h of y - 2/3h(1/2)y^2 + 1/9h^2(1/3)y^3

    = 38/3b^2h

    Thanks in advance.
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  2. #2
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    Re: Find Volume of Solid S

    could you explain what is y?
    The volume of Solid S should be 18h*b^2,
    The volume of a pyramid is 1/3 * Base Area * Height
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  3. #3
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    Re: Find Volume of Solid S

    Quote Originally Posted by piscoau View Post
    could you explain what is y?
    The volume of Solid S should be 18h*b^2,
    The volume of a pyramid is 1/3 * Base Area * Height
    I'm using intergral calculus, or attempting to, to find the volume of the described solid. Using the shells method. So y is the variable in this case denoting the height of the solid if rotated about the y-axis.
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  4. #4
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    Re: Find Volume of Solid S

    I think I figured it out, the limits of integration were were, it should be from a=0 to b=3h
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