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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 x-y 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 x-y plane. The side of the square cross-section for the first solid has length $(9-x^2)$ ... $\displaystyle V = 2\int_0^3 (9-x^2)^2 \, dx$ The second described solid has a rectangular cross-section with base $(9-x^2)$ and height $4$ ... you set this one up. September 13th, 2017, 09:23 PM   #3
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 Originally Posted by skeeter Hopefully, you've sketched the base of the described solids that lie in the x-y plane. The side of the square cross-section for the first solid has length $(9-x^2)$ ... $\displaystyle V = 2\int_0^3 (9-x^2)^2 \, dx$ The second described solid has a rectangular cross-section with base $(9-x^2)$ and height $4$ ... you set this one up.
Ok, so the second one would be:

$\displaystyle V = 2\int_0^3 4(9-x^2) \, dx$ September 14th, 2017, 04:23 AM   #4
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 Originally Posted by nbg273 Ok, so the second one would be: $\displaystyle V = 2\int_0^3 4(9-x^2) \, dx$
Correct ... I hope you noted the use of each solid's symmetry w/respect to the y axis in setting the limits of integration. Tags base, find, region, solid, volume Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Dylanrockin Calculus 2 February 6th, 2017 07:46 AM alex83 Calculus 6 March 5th, 2009 09:58 AM bobber Calculus 1 December 13th, 2008 07:54 AM mmmboh Calculus 1 November 2nd, 2008 04:54 PM gretschduojet Calculus 1 August 19th, 2007 12:40 AM

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