63944f…: “Besides a stormy river”

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Set-up integrals in rectangular, cylindrical, and spherical coordinates that will compute the volume of the cone with a cap shown below:

$\int _{\answer {-2}}^{\answer {2}}\int _{\answer {-\sqrt {4-x^2}}}^{\answer {\sqrt {4-x^2}}}\int _{\answer {\sqrt {x^2+y^2}}}^{\answer {\sqrt {8-x^2-y^2}}}\d z \d y \d x$ $\int _{0}^{\answer {2\pi }}\int _{\answer {0}}^{\answer {2}}\int _{\answer {r}}^{\answer {\sqrt {8-r^2}}} r\d z \d r \d \theta$ $\int _{0}^{\answer {2\pi }}\int _{0}^{\answer {\pi /4}}\int _{\answer {0}}^{\answer {\sqrt {8}}} \rho ^2\sin (\varphi )\d \rho \d \varphi \d \theta$