# Homework Help: Solids of revolution question

1. Feb 20, 2013

### lionely

1. The problem statement, all variables and given/known data
Find the volume of the solid generated by rotating about the y-axis
y= 1-x3 x=0 , y=0

I tried sketching the graph of y= 1-x^3 then tried to find the volume from y=1 to y=0.

if x^3 = 1-y
x= (1-y)1/3
so x2= (1-y)2/3

∏∫x2δy

=> ∏∫(1-y)2/3.dy = ∏[ -3/5(1-y)^(5/3)]

I did that for y=1 to y=0.
But I can't get the right answer.

I got 0pi
but the answer should be 3pi/5

Last edited: Feb 20, 2013
2. Feb 20, 2013

### eumyang

It would be helpful if you told us what answer you got and what answer you are supposed to get.

3. Feb 20, 2013

### lionely

I edited it

4. Feb 20, 2013

### eumyang

The antiderivative looks right, so it looks like the error is in substituting the y = 1 and y = 0. Double check your work.

5. Feb 20, 2013

### lionely

omg I'm so stupid I didn't do the one for 0, because most times when it's 0 I ignore it. Bad a habit. I got 3/5pi now

Last edited by a moderator: Feb 20, 2013
6. Feb 20, 2013

### haruspex

What did you get for each bound (y=0, y=1)?

7. Feb 20, 2013

### lionely

I got it now!