Question

In Exercises \(9-14,\) find an equation in cylindrical coordinates for the equation given in rectangular coordinates. $$ x^{2}+y^{2}+z^{2}=10 $$

Short answer

The equation in cylindrical coordinates will be \(r^{2}+z^{2}=10\).

Step-by-step solution

Identify the relationship between coordinate systems

The relationship between rectangular and cylindrical coordinates is \(x^{2}+y^{2}=r^{2}\) and \(z=z\).

Substitute the relationship into given equation

Substitute the relationships into the given equation \(x^{2}+y^{2}+z^{2}=10\). The left-hand side of the equation \(x^{2}+y^{2}+z^{2}\) can be replaced with \(r^{2}+z^{2}\). This yields the equation \(r^{2}+z^{2}=10\).