Question

What is the equation of a sphere in cylindrical coordinates?

Answer 1

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`.

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