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October 2nd, 2008, 09:04 PM   #1
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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
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October 3rd, 2008, 03:29 PM   #2
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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.
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October 3rd, 2008, 03:51 PM   #3

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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 x-axis is an isosceles triangle with hypoteneuse across the base. Find the volume."


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 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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