Is it possible to define a differentiable manifold structure on a cone?

Question

A cone is a topologic manofold but can we define a differentiable manifold structure on it?

Answer 1

The projection $p$ from the cone onto the $x,y$-plane is a homeomorphism. So you can use $p$ to pull back the differential manifold structure on the $x,y$-plane and you get a differential manifold structure on the cone.