# Finding the Volume

1. May 23, 2005

### ziddy83

Hey everyone...I need to find the volume of the following shape...

$$y= \frac{1}{x}, y=0, x=1, x=3$$

rotated about $$y=-1$$

ok so, i drew out the shape, and for the radius i came up with:

$$r= \frac{1}{x} + 1$$

I think thats correct...so assuming that my radius is right, then the volume would be...

$$\pi \int_{1}^{3} ( \frac{1}{x} +1)^2 dx$$

did i set this up right? Thanks..

2. May 24, 2005

### whozum

http://tutorial.math.lamar.edu/AllBrowsers/2413/VolumeWithRings.asp [Broken]

Check out examples 3 and 4.

Last edited by a moderator: May 2, 2017
3. May 24, 2005

### OlderDan

Your solid has a hole in the middle. The y = 0 boundary excludes a cylinder of radius 1 from the solid. You need the difference of the squares of the outer radius and inner radius.