November 10th, 2014, 10:02 AM  #1 
Newbie Joined: Nov 2014 From: Texas Posts: 6 Thanks: 0  volume xaxis vs yaxis
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 yaxis". 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, 11:21 AM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
Correct answer is A. Use the formula: Last edited by skaa; November 10th, 2014 at 11:23 AM. 
November 10th, 2014, 11:23 AM  #3 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
$\displaystyle V=\pi \int_{0}^{8}(y^{\frac{1}{3}})^2dy=\pi \int_{0}^{8}y^{\frac{2}{3}}dy=\frac{3}{5}\pi y^{\frac{5}{3}} _0 ^8$


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volume, xaxis, yaxis 
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