Like this paraboloid, for example. The equation is z = -(x² + y²) + 10. The cross section is a circle of radius √[-z + 10] = x² + y². The circumference is then 2π√[-z + 10] = x² + y².

You then integrate the circumference multiplied by the differential of z, dz.

In coming up with this example, I've realized a deficiency in my instruction that I'm sure will be filled at a later date, but I want to know now. How would I set up said integral? Always before when I've done problems like this, they've given me a nice neat expression for r. Now...I don't know.

]]>I'm still not quite sure how that works. But I'll turn it over in my head a while to see if I can get it to make sense.

]]>Oh, how do you generate those images that you use. I am behind the times and would love to make such diagrams. I understand the uploading and such, just not the creation of the image itself. Is there a piece of software that you would recommend to me?

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∫2πf(x)√(1 + [f'(x)]²) dx

It is basically a circumference times the arc length.

I will say that the original post seemed more like a related rate problem though.

]]>Anyways, yeah that pic didn't come through. Give it another shot if you will.

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