October 2nd, 2008, 08:04 PM  #1 
Joined: Oct 2008 Posts: 1 Thanks: 0  Find the volume of the solid
Find the volume of the solid s The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Crosssections perpendicular to the xaxis are isosceles right triangles with hypotenuse in the base. Some help please 
October 3rd, 2008, 02:29 PM  #2 
Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Find the volume of the solid
Unless I'm wrong, there is not sufficient information. I'm thinking it's an elliptical cone with the apex on the zaxis ...but it doesn't state how far along in that direction. You can't find volume if all you have is the base.

October 3rd, 2008, 02:51 PM  #3 
Guest Joined: Posts: n/a Thanks:  Re: Find the volume of the solid
Yes, Dave, we can find the volume. This is not a volume of revolution. Here is a similar problem. Use this to see if you can figure out yours...OK. "The base of a solid is the region enclosed by . Every cross section perp. to the xaxis is an isosceles triangle with hypoteneuse across the base. Find the volume." SOLUTION: Use the formula for the area of the triangle and sub it into the integral. We get Can you try yours now?. You have an ellipse with minor axis of length 2 along the xaxis. A lot of times we see these problems with semicircles as cross sections, squares, equilateral triangles, and so forth. For a semicircle we would use the area of a semicircle, etc. 

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