My Math Forum Find the volume of the solid

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 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. Cross-sections perpendicular to the x-axis 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 z-axis ...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 $y=\frac{1}{x}, \;\ y=0, \;\ x=1, \;\ x=3$. Every cross section perp. to the x-axis 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 $\frac{1}{2}\left(\frac{1}{2}\cdot\frac{1}{x}\right )\left(\frac{1}{x}\right)=\frac{1}{4x^{2}}$ $V=\int_{1}^{3}\frac{1}{4x^{2}}dx=\frac{1}{6}$ Can you try yours now?. You have an ellipse with minor axis of length 2 along the x-axis. 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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