The model pictured on the left is the solid obtained by revolving the region between the graph of y=(x-1)(x-3)^2 and the x-axis on [1,3] around the y-axis. The model in the back is an approximation of that solid using 8 shells, and the model on the right is an approximation with 16 shells.
This particular volume is the same one computed with a definite integral at , in case you feel like doing some calculus.
For more information about the math behind approximating volumes with shells, see the link below. MakerHome, Day 238: ...
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Shell approximation of solid of revolution II
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