# 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=8x# and x=2 revolved about the x=4?

##### 1 Answer

Please see below.

#### Explanation:

Here is a sketch of the region. To use shells, we'll take a representative slice parallel to the axis of rotation. (Parallel to the line

The slice is taken at some value of

The volume of the representative shell is

In this case,

the radius

The height of the slice is the upper

Solving

So,

The volume of the representative shell is

# = 8pisqrt2 int_0^2 (4-x)sqrtx \ dx#

# = 896/15 pi#