Volume of this by shell method

**fattydq** · February 24th 2009, 05:39 PM

I know the formula would be V=2pirhdr but I don't understand what that means when you're given a problem with two functions rotated around some line, how do I derive the radius and height and change of radius from that? I've read through my book and I'm clear on everything up to finding volumes this way, but they seem to be very sloppy in explaining this method.

**fattydq** · February 24th 2009, 05:43 PM

I've posted a picture of the one I'm working on and I have the 3d model sketched out. Now what? Could someone walk me through or at least get me started?

**skeeter** · February 24th 2009, 05:57 PM

cylindrical shells about the x-axis ...

$V = 2\pi \int_0^2 y\left(\frac{y^2}{4}\right) \, dy<br />$

or, washers about the x-axis ...

$V = \pi \int_0^1 (2)^2 - (2\sqrt{x})^2 \, dx$

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