# How do you determine the volume of a solid created

How do you determine the volume of a solid created by revolving a function around an axis?
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Belen Bentley
Given a function f(x) and an interval [a,b] we can think of the solid formed by revolving the graph of f(x) around the x axis as a horizontal stack of an infinite number of infinitesimally thin disks, each of radius f(x).
The area of a circle is $\pi {r}^{2}$, so the area of the circle at a point x will be $\pi f\left(x{\right)}^{2}$
The volume of the solid is then the infinite sum of the infinitesimally thin disks over the interval [a,b]
So:
Volume $={\int }_{a}^{b}\pi f\left(x{\right)}^{2}dx=\pi {\int }_{a}^{b}f\left(x{\right)}^{2}dx$