# Method of cylindrical shells

by ktpr2
Tags: cylindrical, method, shells
 P: 192 I know one can figure the volume of a torus by the difference of two volumes, but I'm trying out the method of cylinderical shells. As far as i understand, you can often create a primitive with a calcuable volume and approximate the volume of the shape you wish by scaling the primitive along the curve it creates, adding infintely many times. The problem is that my answer is wrong when i try to set up an integral when thinking in terms of cylinderical shells: We have a rectangle, bent in the shape of a circle, with length $$2 \pi r$$ height $$\sqrt{1-x^2}$$ and width$$\Delta x$$, so it's volume should be all that multiplied together. I have torus radius (this torus is just a circle, really) of R and the circle being revolved has a radius of r. So my integral is: $$\int_{R-r}^{R+r} 4 \pi x \sqrt{1-x^2} \Delta x$$ and the above is off by $$r^3 R$$ when i use differences of two volumes, what conceptual flaw am I making?