# How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y = sqrt(x)#; #y = 0#; and #x = 4# rotated about #y=6#?

##### 1 Answer

Sep 26, 2015

See the explanation section below.

#### Explanation:

Here is a picture of the region and the line

I've tried to show a representative slice to use cylindrical shells.

The thickness of the shell is

The curve

In the region,

At each value of

and the 'height' of the shell (it is lying on its side) will be the greater

The volume of a representative shell is

So we need to integrate:

Expand the polynomial and integrate term by term to get