My Math Forum volume x-axis vs y-axis

 Calculus Calculus Math Forum

 November 10th, 2014, 11:02 AM #1 Newbie   Joined: Nov 2014 From: Texas Posts: 6 Thanks: 0 volume x-axis vs y-axis Hello again Math Forum community! I am already liking this bunch of people. So I am working on some volume problems and I am understanding most of context, but I am getting hung up on which formula to use for x vs y axis rotations. Example: "Find the volume of the region by revolving the region about the y-axis". The region enclosed by $\displaystyle x=y^\frac13, x=0, y=8$ A. $\displaystyle \frac{96}5\pi$ B. $\displaystyle 32\pi$ C. $\displaystyle 16\pi$ D. $\displaystyle 12\pi$ So which values do I use for the bounds of the integral? $\displaystyle \int_0^{y^\frac13}$????? And will the formula look like the following?: $\displaystyle \int_0^{y^\frac13}2\pi x {8}$ Do I have this backwards?
 November 10th, 2014, 12:21 PM #2 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 211 Thanks: 76 Correct answer is A. Use the formula: Last edited by skaa; November 10th, 2014 at 12:23 PM.
 November 10th, 2014, 12:23 PM #3 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 211 Thanks: 76 $\displaystyle V=\pi \int_{0}^{8}(y^{\frac{1}{3}})^2dy=\pi \int_{0}^{8}y^{\frac{2}{3}}dy=\frac{3}{5}\pi y^{\frac{5}{3}} |_0 ^8$ Thanks from thesheepdog

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