A rectangular tank that is $4$ meters long, $3$ meters wide and $6$ meters deep is filled with a rubbing alcohol that has density $\backslash (786\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ In each part below, assume that the tank is initially full, and that gravity is $\backslash (9\mathrm{.}8\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$

Enter exact answers. Your answers must include the correct units.

$($a$)$ How much work is done pumping all of the liquid out over the top of the tank?

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$($b$)$ How much work is done pumping all of the liquid out of a spout $1$ meters above the top of the tank?

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$($c$)$ How much work is done pumping two$-$thirds of the liquid out over the top of the tank?

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