What should be the shape of elemental part while finding the volume of a given shape formed by revolving a 2-D curve, y = f(x). Should I take it as frustum of cone or a cylinder ? Which and why only that and not other ? If frustum are to be chosen as elemental part then why in some cases like Gabriel's cone, method of choosing cylindrical elemental part also works ? Please explain it in detail I am just a beginner in maths and having only a little knowledge of calculus ?
2026-03-30 23:11:13.1774912273
Volume and area of silids
35 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The reason we use disks or cylindrical shells to find the volume of a solid of revolution is that they are simple shapes and solids of revolution themselves. The rules for the volume of a single disk or shell are simple. Often the limits to use are simple as well.
Presumably when you suggest using frustrums you are thinking about a differentially thin outer shell of the frustrum of a cone, with all the cones having a common angle at the peak. This is a fine approach if it accounts for all the volume of your solid and only accounts for each part of it only once. The equation for the volume of an individual frustrum is a little more complicated than disks or cylinders, but if your shape is one that it is much easier to get the limits right because they fit it naturally, that is a fine idea.