Answer
sphere with radius $2$ and center at origin.
Work Step by Step
In the cylindrical coordinate system, we have $x=r \cos \theta \\ y=r \sin \theta \\z=z$
Conversion of rectangular to cylindrical coordinate system, we have $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
As per problem, then we get $x^2+y^2+z^2=4$ when $r^2=x^2+y^2$
So, $x^2+y^2+z^2=4$
Re-arrange as: $x^2+y^2+z^2=2^2$
Hence, we have an equation of a sphere with radius $2$ and center at origin.
