volume using cross-sections

label Calculus
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schedule 1 Day
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find the volume of the solid generated by revolving the region about the y-axis. the region enclosed by x=y^2/3, x=0, y=-3,y=3....... i need every step.

May 20th, 2015

Here is the graph of the region

https://www.desmos.com/calculator/hnvlft8ofa

So the way I did it was since I know the graph is being rotated around the y-axis, I know that we are dealing with circles as cross sections. So now I need to know how much of each circle is contained in the region. So the region revolved to the y-axis is a quarter rotation, So the cross sections will be quarter circles. So now we have the integral from 3 to 0 of the equation 1/4pi(y^2/3)^2 dy. Put the 1/4pi on the other side for now and take the integral from 3 to 0 of y^4/9 dy, which is y^5/45 = 243/45 x 1/4pi. Since this is one eight of the total volume multiply this value by 8 to get 486pi/45. I hope this is right. Let me know if you have any questions.


May 20th, 2015

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May 20th, 2015
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May 20th, 2015
Jun 29th, 2017
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