12.2a Oblique Lateral Areas

Shown is an oblique circular cylinder. Clicking "Rearrange" rearranges the oblique circular cylinder into a right elliptic cylinder, whose lateral area is equal to that of the oblique circular cylinder and is relatively easy to calculate. Notice that the lateral area of the oblique circular cylinder is [i][b]not[/b][/i] [math]p\ell[/math], where [math]p[/math] is the perimeter of the oblique circular cylinder's base and [math]\ell[/math] is its slant height. The same technique can be used to find the lateral area of an oblique prism. However, it can not be used to find the lateral area of an oblique pyramid or cone, which is too complicated to discuss in this course.

Cavalieri's Principle

If two bodies have equal cross-sections in each height, their volumes must be equal.
Cavalieri's Principle

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