Shell approximation of solid of revolution II Free 3D print model

cgtrader

The solid displayed on the left-hand side of the diagram is the three-dimensional object that results from rotating the area between the graph of y=(x-1)(x-3)^2 and the x-axis on [1,3] about the y-axis. The two models visible in the background represent approximate calculations of this solid, each utilizing 8 shells to estimate its overall shape, while the model situated on the right is based on an approximation made using 16 such shells. For those who are mathematically inclined and wish to compute the same volume via definite integral, a step-by-step explanation can be found on https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/shell-method/v/shell-method-for-rotating-around-vertical-line. To gain further insight into the process of approximating volumes using shells, readers are invited to visit MakerHome at http://makerhome.blogspot.com/2014/04/day-238-shellmaker-2.html for additional information and detailed analysis.