# How do you use the disk or shell method to find the volume of the solid generated by revolving the regions bounded by the graphs of #y = x^(1/2)#, #y = 2#, and #x = 0# about the line #x = -1#?

##### 1 Answer

See the explanation section, below.

#### Explanation:

Here is a picture of the region with a thin slice taken vertically.

So thickness is

The representative shell will have volume

We see that the values of

So the volume of the solid is found by evaluating:

Expand the product and integrate term by term.

**To use disks/washers** , we need to take our slices perpendicular to the axis of rotation as shown below.

The curve is now expressed as

The representative washer has volume:

Again, expand and integrate term by term.