How do you find the volume of a pyramid using integrals?

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Answer 1 · 2014-10-02T07:55:40

Let us find the volume of a pyramid of height #h# with a #b\times b# square base.

If #y# is the vertical distance from the top of the pyramid, then the square cross-sectional area #A(y)# can be expressed as

#A(y)=(b/hy)^2=b^2/h^2y^2#.

So, the volume #V# can be found by the integral

#V=int_0^hA(y) dy=b^2/h^2int_0^hy^2 dy=b^2/h^2[y^3/3]_0^h =1/3b^2h#.

I hope that this was helpful.