I have this task: Calculate the moment of inertia of a homogeneous body $G$, bounded by the surface $\{(x^2+y^2+z^2)^2=a^3z,\, a>0\}$ (image) relative to the axis of the application $OZ$. In the solution, we move to spherical coordinates, in which we set the following boundaries for the new body: $\Omega:\{0\leq \varphi \leq 2\pi, 0 \leq \theta \leq \pi/2, 0 \leq \rho \leq a\sqrt[3]{\cos \theta}\}$ (image). Why do we have such limits for phi and theta?
2026-03-29 21:13:33.1774818813
The moment of inertia: limits for angles.
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