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Calculate the volume of a ice cream cone inside a cone $z=5\sqrt{x^2 + y^2}$ and paraboloid $z=\frac 92 -2x^2 -2y^2$. in cylindricals $$5\sqrt{x^2 + y^2}=\frac 92 -2x^2 -2y^2$$ $$5\sqrt{r^2(\cos^2\phi + \sin^2\phi)}=\frac 92 -2r^2(\cos^2\phi+\sin^2\phi)$$ $$5r=\frac 92 -2r^2$$ $$r=\cases{ \frac 14(-5-\sqrt{61}) \\ \frac 14 (-5+\sqrt{61})}$$

$$V=\int_0^{2\pi}d\phi\int_0^{\frac 14 (-5+\sqrt{61})}1rdr\int_{r}^{\frac{9}{10}-\frac 25r^2}dz$$

Makes any sense?

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Hint: I suggest you use cylindrical coordinates to simplify the calculation.

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