Question

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis:

y=(x-2)^3-2, x=0, y=25

Solve by either the disk or washer method.

I calculated the volume using the shell method and got 1250pi. However, I can't figure out how to calculate it using the disk method. The answers should be the same unless I calculated the volume using the shell method incorrectly.

Answer 1

I redid my shells because of a typo, and I got

2π∫[0,5] x(25-((x-2)^3-2)) dx
= 500π

How did you get 1250π? What was your integral?
We need to integrate over x, because the thickness of the shells is dx, not dy.

As for discs,
x = ∛(y+2) + 2

v = π∫[-10,25] πx^2 dy
= π∫[-10,25] (∛(y+2) + 1)^2 dy
= 500π

Answer 2

I also checked my calculation in our previous post
http://www.jiskha.com/display.cgi?id=1385311297

I carelessly dropped the π in my last 3 lines, and should have used my calculator to add up the terms in my last line.
<b>My last line should have been 500π</b>

which then also agrees with Steve's new answer using shells

So you have your two methods,
mine using disks
Steve's using shells
both 500π