A special table in Jim's high school chemistry lab pumps liquid methane from an inverted conical reservoir into a series of test tube located $50$ cm above the top of the reservoir. The reservoir is $40$ cm deep and has a base radius of $35$ cm $.$

If the reservoir is initially filled to capacity, the density $\backslash (\backslash$rho $\backslash )$ of the methane is $\backslash (420\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ and the acceleration due to gravity is approximated as $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ calculate the amount of work required by the table's pump to completely empty the contents of the reservoir into the test tubes.

Give the exact answer. Do not round.