Question

Find the volume of the solid generated by revolving the region about the y-axis.

The region in the first quadrant bounded on the left by y = 3/x , on the right by the line x=3 , and above by the line y = 2

Answer 1

Can someone help me set up this problem? Im having trouble graphing it.

Answer 2

Here is a graph (I used geogebra... see http://www.geogebra.org/cms/en/ )

Answer 3

notice that from y=0 to 1, you have a constant radius of x=3
it has the volume of a cylinder of height 1, and radius 3

now use calculus to find the volume of the region above y=1

Answer 4

do you know how to integrate volume using the shell method or disc method ?

Answer 5

Yes, I know the formula, Im still just having trouble picturing it.

Answer 6

im revolving around the y axis. So i'm integrating from 0 to 3 right?

Answer 7

first, which technique are you using ?

Answer 8

I need to use the disk method right?

Answer 9

ok, for the disc method we have two regions (because the radius is not defined by the same function)

First, what is the volume of the cylinder with radius=3 and height 1
you don't need calculus but you can use calculus if you want. I would use geometry and if I wanted to use calculus to see if I get the same answer.

Answer 10

9pi sorry.