A typical cylindrical shell (in green) is also shown and can be animated. The animation demonstrates how the volume of the solid is approximated by the sum of volumes of cylindrical shells.

Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

If we partition the interval from x = 0 to x = 1 into parts and draw a resulting rectangle, then by revolving the rectangle about the y-axis, we see that a shell is generated. In the figure below, drag the slider to …

I use manipulables and 3D animation to help visualize how the Shell method works to compute the volume of a solid of revolution with integrals.

An interactive 3D graphing calculator in your browser. Draw, animate, and share surfaces, curves, points, lines, and vectors.

Master the shell method for calculating volumes of revolution through a foolproof, step-by-step approach that simplifies cylindrical shell visualization, radius identification, and height determination in calculus …

Subscribed 416 48K views 10 years ago animation showing the concept of shell method of volumes...more

The idea of the shell method is to picture the solids instead as being made up of thin cylindrical shells which sweep outward from the central axis and fill up the solid.

Feb 2, 2026 · Calculate volumes of revolution using the Shell Method with step-by-step solutions and detailed analysis for calculus applications.

Find the volume of the solid formed by revolving the region tounded by the graphs y = 0, —O, and x = I about the y-axis, as shown in Figure 7.21. 7.21 Solid of (1.2) . Author. Yang, David M . Created Date. …