I am supposed to find the volume of a torus with radii r and R using cylindrical shells. I don't even know what a torus is, and the whole shell method is still confusing to me.

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- Oct 21st 2008, 08:06 PMsfgiants13Finding the Volume of a Torus
I am supposed to find the volume of a torus with radii r and R using cylindrical shells. I don't even know what a torus is, and the whole shell method is still confusing to me.

- Oct 22nd 2008, 08:00 AMshawsend
The plot is a cross-section of a torus showing a cross-section of one of the cylindrical shells (thick black walls) we'll use to calculate the volume. The equation of the cross-section on the right is:

or

and the formula for calculating the volume using cylindrical shells is:

Now, in this case, that would be:

since we're integrating only the top half right?

which is messy and also you get an component which you have to take the limit of as x goes to either limit. Eventually you get:

Maybe an easier way though.