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September 13th, 2017, 05:38 PM  #1 
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  Find the volume of the solid whose base is the region...
Find the volume of the solid whose base is the region in the xy plane bounded by y=x^2, y=9, and x=0, and whose cross sections perpendicular to the x axis are: a) squares b) rectangles with a height of 4 I missed a single class and this is on the homework which I have no idea how to do. I've never even heard of a cross section so I assume this is something they talked about in class. Can someone at least show me how to set up the problem and I think I can figure out the answer from there. Thanks, everyone. 
September 13th, 2017, 07:40 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 
Hopefully, you've sketched the base of the described solids that lie in the xy plane. The side of the square crosssection for the first solid has length $(9x^2)$ ... $\displaystyle V = 2\int_0^3 (9x^2)^2 \, dx$ The second described solid has a rectangular crosssection with base $(9x^2)$ and height $4$ ... you set this one up. 
September 13th, 2017, 09:23 PM  #3  
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  Quote:
$\displaystyle V = 2\int_0^3 4(9x^2) \, dx$  
September 14th, 2017, 04:23 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677  

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base, find, region, solid, volume 
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