# Homework Help: Find the volume of the solid

1. Mar 23, 2014

### jsun2015

1. The problem statement, all variables and given/known data
Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about the line y=1

2. Relevant equations
V= integral of pi*r^2 from a to b with respect to variable "x"

3. The attempt at a solution
pi(integral of 1-(x^2-1)^2 from 0 to 1 dx)

2. Mar 23, 2014

### Dick

Why do you think the 'r^2' part in your volume equation is 1-(x^2-1)^2 and why do you think the limits to the integration are 0 to 1?

3. Mar 23, 2014

### jsun2015

r^2

limits to integration
the radius of the sphere is on the region x= 0 to 1

4. Mar 23, 2014

### jsun2015

r^2

limits to integration
the radius of the sphere is on the region x= 0 to 1

5. Mar 23, 2014

### Dick

That's confusing me. The formula you gave was actually for the method of disks, which is what I would use here. If you are rotating the region between y=x^2 and y=1 around y=1, then the inner radius is 0, isn't it? And I don't see why you are putting one of the limits to 0. y=x^2 and y=1 cross at x=1 and x=(-1), yes?

6. Mar 23, 2014

### jsun2015

Yes. Yes. I came up with my original answer because at the outer region 1= radius so we have one and at the inner region 0 = radius as (1^2-1)^2=0

I have only studied the washer method.

7. Mar 23, 2014

### jsun2015

Yes. Yes. I came up with my original answer because at the outer region 1= radius so we have one and at the inner region 0 = radius as (1^2-1)^2=0

I have only studied the washer method.

8. Mar 23, 2014

### Dick

The disk method is the same as the washer method with an inner radius of 0. Isn't the outer radius ALWAYS 1-x^2? And the inner radius 0?

9. Mar 23, 2014

### jsun2015

I correct myself, I have studied disc method. Yes. yes.

10. Mar 23, 2014

### jsun2015

I correct myself, I have studied disc method. Yes. yes.