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Find the volume of a pyramid with height h and rectangular base with dimensions b and 2b.

Essentially, I'm trying to derive the volume of a pyramid using integrals and a graph and revolving the plane about an axis. I hope that's kind of clear and you guys understand what I'm asking.

Thank you very much

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  1. That seems to me to be the hard way to integrate.

    take a small rectangular box dV somewhere along the height.

    dV= dh*darea
    darea= dw dl=(H-h)(b)*(H-h)2b /H^2

    dV=1/H^2 (H-h)^2 2b^2 dh h from 0 to H

    V= 2b^2/H^2 INT (H-h)^2 dh= 2b^2 /3 H^2 *(H-h)^3 from zero to H
    =2b^2/3 H

    which you knew, the volume of any rectangular prism is 1/3 area base*height

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