(a) Use differentials to find a formula for the approximate volume of a thin cylindrical shell with height
, inner radius
, and thickness
.
This part is fairly simple--
, assuming
is a constant. This yields
.
(b) What is the error involved in using the formula from part (a)?
This is where I'm stuck. The formula in part (a) assumes
is a constant, and thus doesn't account for the change in
, even though the thickness does affect the top of the shell. Seeing this, I would assume the error to be in the volume of the "lid", or
. However, my book gives me an answer of
. What am i doing wrong?