  Do and Norbury found a so-called differential relation which relates the
volume of the moduli space of singular surface with a cone point to that of a
smooth surface obtained by forgetting the cone point. Their procedure is valid
for cone angles less than $\pi$ by work of Tan, Wong and Zhang. We study the
moduli space of a surface with a single cone point of angle ranging from $0$ to
$2\pi$ using a coordinate system closely related to Penner's $\lambda$-lengths.
We compute the action of the mapping class group in these coordinates, give an
explicit expression for Wolpert's symplectic form and use this to justify Do
and Norbury's approach using just hyperbolic geometry.
