# How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y^2=4x#, x=y revolved about the y-axis?

##### 1 Answer

See below.

#### Explanation:

Draw a picture (sketch) of the region.

Note that the graphs intersect where

And that happens at

We are asked to use shells, so we take thin representative rectangles parallel to the axis of rotation. In this case that is the

The slice has solid black boundaries and the radius to the axis of rotation is shown as a dashed black line.

Since the thin part is

The lower function is

The volume of a representative shell is

In this case, we have

radius

height

(details left to the student)

# = (128pi)/15#