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September 13th, 2017, 04:38 PM   #1
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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.
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September 13th, 2017, 06:40 PM   #2
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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.
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September 13th, 2017, 08:23 PM   #3
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Quote:
Originally Posted by skeeter View Post
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:

$\displaystyle V = 2\int_0^3 4(9-x^2) \, dx$
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September 14th, 2017, 03:23 AM   #4
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Originally Posted by nbg273 View Post
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.
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