Find the volume of the solid of revolution generated by revolving the region bounded by y=2x^2, y=0, and x=2 around the line y=8.

The answer should be 187.658

Question

Find the volume of the solid of revolution generated by revolving the region bounded by y=2x^2, y=0, and x=2 around the line y=8. 

The answer should be 187.658

anonymous · Answer

You'll be amazed a simple sketch can help

anonymous · Answer

@sourwing  I did sketch it, but I don't know what my radii should be. I only know how to revolve lines around the y-axis, x-axis, and vertical lines. I'm not sure how to revolve it around a horizontal line.

anonymous · Answer

|dw:1396480380468:dw|

anonymous · Answer

what is the outer radius?

anonymous · Answer

8?

anonymous · Answer

good. What is the inner radius?

anonymous · Answer

8-(2x^2)?

anonymous · Answer

there you go. Plug and chug

anonymous · Answer

pi ∫(outer radius)^2 - (inner radius)^2

anonymous · Answer

When I did it, I got the answer, but as a negative. Is something backwards?

anonymous · Answer

@sourwing

anonymous · Answer

https://www.wolframalpha.com/input/?i=pi+integral+%288%29%5E2+-+%288+-+2x%5E2%29%5E2%2C+x+%3D+0..2 Probably just some algebraic error.

anonymous · Answer

omg how did you find that?

anonymous · Answer

find what ?

anonymous · Answer

the site

anonymous · Answer

this site has been around for years. Any college kid would know

anonymous · Answer

Did you actually know how to find the radii, or did you use the site? @sourwing

anonymous · Answer

O.O 

That's was a rather strange question. I had to know the radii so that I type the equation in Wolfram Alpha

anonymous · Answer

oh no sorry, I was just curious because I have other problems on a worksheet and I was wondering how long you would be on here so I could ask you anymore questions