<s>[INST] How to calculate the volume given by $(x^2+y^2+z^2)^2 = x^2+y^2$ I am working on the following exercise:

Calculate the volume of the body bounded by the following surface:
$$(x^2+y^2+z^2)^2 = x^2+y^2$$

I would solve this with a triple integral, but I do not see how I can derive the boundaries from $(x^2+y^2+z^2)^2 = x^2+y^2$. Could you help me?
 [/INST] HINT
Consider the transformation $x = \rho\cos(\theta)$, $y = \rho\sin(\theta)$ and $z = z$. Then you have
\begin{align*}
(x^{2} + y^{2} + z^{2})^{2} = x^{2} + y^{2} & \Longleftrightarrow z^{2} = \pm\sqrt{x^{2} + y^{2}} - x^{2} - y^{2}\\
& \Longleftrightarrow z^{2} = \pm\rho - \rho^{2} \Longleftrightarrow z^{2} = \rho - \rho^{2}
\end{align*}
since $z^{2} \geq 0$.
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