Argh I just typed up an entire question and accidentally closed the window. Let's try this again.(adsbygoogle = window.adsbygoogle || []).push({});

My friend and I have been pondering this for a while, and hopefully someone will be able to help us out.

When you find the volume of a solid of revolution, you can use the disk method:

[tex]V = 2\pi \int_a^b [R(x)]^2\,dx[/tex]

The volume element in the integral is the volume of acylinderwith height dx.

When you find the area of a surface of revolution, you use the following formula:

[tex]A = 2\pi \int_a^b R(x)\sqrt{1+(\frac{dy}{dx})^2}\,dx[/tex]

The area element in the integral is the lateral surface area of afrustum of a cone. Why doesn't this integral, too, use a cylinder, as the volume integral did? Why does one method use cylinders, and one method use frustums?

Thank you in advance :)

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# Integrals of surface area/volume

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