**Download Volume Using Cross Sections Background**. Steps for finding the volume of a solid with a known cross section. How does the sketch of this even look like?

This page explores volumes where the cross section is known, but isn't generated by revolution, using integral calculus. Find the volume of the solid whose base is the region inside the circle x 2 + y 2 = 9 if cross sections taken perpendicular to the. In the previous section we started looking at finding volumes of solids of revolution.

### • write dv the volume of one representative slice using geometry formulas.

A circular cylinder can be generated by translating a circular disk along a line that is perpendicular to the disk. The volume of a solid with known cross sections can be calculated by taking the definite integral of all the cross sections, with being equal to a single section. The first thing to do is to derive an expression for the surface area of a horizontal cross section of the bowl at an arbitrary level 'd' above the base of. Learn vocabulary, terms and more with flashcards, games and other study tools.