# How do you find the volume bounded by #y=3-x^2# and y=2 revolved about the y=2?

##### 1 Answer

Volume

#### Explanation:

(Sorry if this is in excessive detail)

The given regions in the Cartesian plane look like:

If this is rotated about

we have:

For ease of calculation, it is convenient if we shift this solid down so the axis of rotation falls along the X-axis:

Note that the radius (relative to the X-axis) of this shifted volume is

equal to

and we can slice this solid into thin disks, each with a thickness of

so that each disk has a volume of

With very small values of

We can evaluate this sum with