Computing Volumes using Cross-Sections - Analytic Geometry and Calculus II | Lecture 7

In this lecture we show how definite integrals can be used to compute the volume of three-dimensional shapes. We take cross-sections of a given shape and approximate them using cylinders, leading to a Riemann sum. From the Riemann sum we may pass to a definite integral, putting us firmly in the territory of the previous lectures.

This course is taught by Jason Bramburger for George Mason University.

Course Topics and Goals: At the end of the semester, students should be able to solve various geometry and physics problems that are modelled with definite integrals, use techniques to evaluate integrals, understand infinite series and power series, and be able to identify and graph conic sections and basic parameter and polar curves.

[therosestlwrw]

thank you Mr. Jason for this great video I have a question for the first example why does this method work for pyramids and not cubics even tho it's the same idea? a cross-section for a pyramid is a square and for a cube is a square too, so the area of the base is x^2 for both cubes and pyramids. so why doesn't work for a cube? how do i find the volume of a cube?