Finding the area of a circular strip

[Gabe805]

http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c29/pict_29_93.gif
if I wanted to find the area of the outer circular strip, I know I would just take the area of the composite and subtract out the inner radius. (i.e. pi(a^2)-pi(b^2)). However why can't I use 2pi*radius*thickness? this would be 2pi*a(a-b) which is obviously not the same.

 

[blue_leaf77]

However why can't I use 2pi*radius*thickness? this would be 2pi*a(a-b) which is obviously not the same.

Of course not if the thickness is not infinitesimal. The "2pi*radius*thickness" comes from assuming that the strip can be stretched out to make a long rectangle, which is obviously not possible if the inner and outer radius are not infinitesimally different.

 

[Gabe805]

Of course not if the thickness is not infinitesimal. The "2pi*radius*thickness" comes from assuming that the strip can be stretched out to make a long rectangle, which is obviously not possible if the inner and outer radius are not infinitesimally different.

Yeah, I had a hunch it had something to do with that. If the inner and outer radii are different, then it doesn't wind up being a rectangle. Thanks for the reply.