# What is the equation of a sphere in cylindrical coordinates?

Nov 2, 2014

An equation of the sphere with radius $R$ centered at the origin is

${x}^{2} + {y}^{2} + {z}^{2} = {R}^{2}$.

Since ${x}^{2} + {y}^{2} = {r}^{2}$ in cylindrical coordinates, an equation of the same sphere in cylindrical coordinates can be written as

${r}^{2} + {z}^{2} = {R}^{2}$.

I hope that this was helpful.