Volume of Solid Revolving Region About Line: 32pi/5

[windowsXLC]

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Find the region bounded above by the line y = 4, below by the curve y = 4 - x², and on the right by the line x = 2, about the line y = 4.

The Correct answer was: 32pi/5

I integrated from 0 to 2 of pi [(4)² - (4 - x²)²]

View attachment 8889

and got the answer of 224pi/15.

I tried every other possible ways and still didn't get the answer of 32pi/5.

 

[MarkFL]

Your result would indeed be correct if you were revolving the bounded area about the \(x\)-axis, but you are to revolve the area about the line \(y=4\). Try that, and you'll get the required result. :)