Finding Volume Using Integration: Revolving Functions Around a Line

[EngnrMatt]

Homework Statement

Find the volume of the solid formed by revolving the functions: y=x² and y=1 about the line y=6

Homework Equations

∏∫(r_o²-r_i²)dx

The Attempt at a Solution

I found the outer radius to be (1-x²)-6 and my inner radius to be -6. Also, the limits of integration were -1 and 1. Plugging it all in got -224/15. This is obviously wrong because it is negative, and the positive value didn't work either. Does anyone have a clue on how to do this?

 

[Dick]

Homework Statement

Find the volume of the solid formed by revolving the functions: y=x² and y=1 about the line y=6

Homework Equations

∏∫(r_o²-r_i²)dx

The Attempt at a Solution

I found the outer radius to be (1-x²)-6 and my inner radius to be -6. Also, the limits of integration were -1 and 1. Plugging it all in got -224/15. This is obviously wrong because it is negative, and the positive value didn't work either. Does anyone have a clue on how to do this?

Isn't the inner radius the distance from y=1 to y=6? Isn't that 5? What's the outer radius?

 

[EngnrMatt]

Yes, you are right. I see now, the outer radius will be the distance between y=6 and the lower function and the inner will be the distance between y-6 and the upper function. It worked by the way, thanks.