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 https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/shell-method/v/shell-method-for-rotating-around-vertical-line, 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: http://makerhome.blogspot.com/...

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