# How do you find the volume of the solid obtained by rotating the region bounded by the curves #x=y# and #y=sqrtx # about the line #x=2#?

##### 1 Answer

Please see below.

#### Explanation:

Here is a graph of the region.

I've taken a slice perpendicular to the axis of rotation. The slice is taken at a variable value of

The thickness of the slice is

The curve on the left (

on the right is the line

Rotating the slice will generate a washer of thickness

volume

where

The outer radius of the washer is the distance between the curve on the left and the line

So

The inner radius is the distance from the line on the right and the line

So

The volume of the representative washer is

evaluate to get

# = pi (8/15) = (8pi)/15#