Perhaps you are thinking of the Schwartz Lantern?
It converges to the cylinder in the Hausdorff metric but its area can be arranged
to head toward $\infty$.
It was mentioned in the earlier MO question, "Convergence of finite element method: counterexamplesConvergence of finite element method: counterexamples."
There is nice applet here showing the lantern rotating.
Here is an image from Conan Wu's blog: