A truncated cone, made of material of uniform resistivity, is given in many introductory physics texts as a nontrivial problem in the computation of resistance. The intended method and answer are incorrect and the problem cannot be solved by elementary means. In this paper, we (i) discuss the physics of current flow in a nonconstant cross‐section conductor, (ii) examine the flaws in the ‘‘standard’’ solution for the truncated cone, (iii) present a computed resistance found from a numerically generated solution for the electrical potential in the truncated cone, and (iv) consider whether any problem exists to which the standard solution applies.