The area is equal to ##\pi * r^2## and the radius ##r## is a function of the length ##r(l)##.
To approximate the change in radius, it is taken over a smaller section ##dl## instead of ##l## and sumed up as an integral:
$$R= \int_{0}^{L} \rho\frac{1}{A} \,dl = \rho \int_{0}^{L}...
For the electrical resistance ##R## of an ideal wire, we all know the formula ##R=\rho * \frac{l}{A}##. However this is only valid for a cylinder with constant cross sectional area ##A##.
In a cone the cross section area is reduced over its height (or length ##l##). What is a good general...