# Volume of a Sphere

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Let's say that we want to find the volume of a sphere of radius using volumes of revolution.

We know that the equation of a circle of radius centered at the origin is

The upper half semicircle is given by

Now, we want to rotate the upper half semicircle around the -axis. This will give us a sphere of radius

We use the washer/disk method to find the volume of the sphere. The volume of the sphere is

Hence, the volume of a sphere of radius is