Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.1 Areas and Volumes by Slices, #17 · Calculus · Applications of integrals

Rotate the ellipse … around the … axis to find the volume…

Rotate the ellipse $x^{2} / a^{2} + y^{2} / b^{2} = 1$ around the $x$ axis to find the volume of a football. What is the volume around the $y$ axis? If $a = 2$ and $b = 1$ , locate a point $(x, y, z)$ that is in one football but not the other.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.1 Areas and Volumes by Slices, #17

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