5d9821…: “Throughout the short town”

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Set-up integrals in rectangular, cylindrical, and spherical coordinates that will compute the volume of the eighth of the sphere $x^2+y^2+z^2 = 81$ where $x$ is negative, $y$ is negative, and $z$ is positive. $\int _{\answer {-9}}^{\answer {0}}\int _{\answer {-\sqrt {81-x^2}}}^{\answer {0}}\int _{\answer {0}}^{\answer {\sqrt {81-x^2-y^2}}}\d z \d y \d x$ $\int _{\pi }^{\answer {3\pi /2}}\int _{\answer {0}}^{\answer {9}}\int _{\answer {0}}^{\answer {\sqrt {81-r^2}}} r\d z \d r \d \theta$ $\int _{\pi }^{\answer {3\pi /2}}\int _{0}^{\answer {\pi /2}}\int _{\answer {0}}^{\answer {9}} \rho ^2\sin (\varphi )\d \rho \d \varphi \d \theta$