# How do you find the volume of the region bounded by #y=6x# #y=x# and #y=18# is revolved about the y axis?

##### 1 Answer

Aug 21, 2015

Use washers. to get

#### Explanation:

The region is the bounded region in:

graph{(y-6x)(y-x)(y-0.0001x-18) sqrt(81-(x-9)^2)sqrt(85-(y-9)^2)/sqrt(81-(x-9)^2)sqrt(85-(y-9)^2) = 0 [-28.96, 44.06, -7.7, 28.83]}

Taking vertical slices and integrating over

Rewrite the region:

As

The greater radius is

Evaluate

# = (35pi)/36 int_0^18 y^2 dy#

# = 1890pi#

(Steps omitted because once it is set up, I think this is a straightforward integration.)