Find the the volume of the solid obtained by rotating the region bounded by the given curves. x=2sqrt(y), x=0, y=9; about the y-axis. I turn x=2sqrt(y) to x^2/4=y and integrate pi(x^4/16) from 0 to 6. the book says the answer is 162pi, but I don't get that.

Question

anonymous · Answer

I got the answer.

dumbcow · Answer

there are 2 ways to do this, disc method or shell method
looks like you used disc method but used the wrong equation, you squared the x^2/4 ...but that is Not the radius
its important to note which axis you are rotating the region around, in this case the y-axis so the circular cross-sections are horizontal...radius is x-distance in terms of y
in other words ,(rotate around y-axis, integrate wrt y)
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