Can you find the area of a hollow cylinder using the equation of a cylindrical shell?

Question

anonymous · Answer

$$V = 2\pi(r)(thickness)(height)$$

anonymous · Answer

So, I am trying to figure out if the volume of a hollow cylinder is equivalent to the volume of a cylindrical shell used in integral calculus.

Hallow Cylinder = $$(\pi)(height)((r _{o})^2-(r _{i})^2)$$
Cylindrical Shell = $$2(\pi)(r _{i})(height)(thickness)$$

The subscript "o" means outer-radius, and "i" means inter-radius

irishboy123 · Answer

this doesn't really make any sense.  to me at least.

what are you trying to achieve?

anonymous · Answer

I think OP is trying to bridge whatever gap there appears to be between the shell and washer methods?

anonymous · Answer

Let's see if I'm understanding the question properly...

Consider two cylinders with equal heights $h$ and radii $r$ and $R$, where $r<R$. Place the smaller inside the larger. You can compute the volume of the space between the two cylinders by subtracting to get the first formula you mentioned: $V=\pi h(R^2-r^2)$.
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