You want to filter an aqueous slurry using a rotary drum filter, at a total rate (of filtrate) of $10,000 \mathrm{gal} / \mathrm{day}$. The drum rotates at a rate of $0.2 \mathrm{rpm}$, with $25 %$ of the drum surface submerged in the slurry, at a vacuum of $10 \mathrm{psi}$. The properties of the slurry are determined from a lab test using a Buchner funnel under a vacuum of $500 \mathrm{~mm} \mathrm{Hg}$, using a $100 \mathrm{~cm}^{2}$ sample of the filter medium and the slurry, which resulted in the data given in the following table. Determine the total filter area of the rotary drum required for this job.

Lab data:

Time (s)	Volume of Filtrate (cc)
50	10
100	18
200	31
400	51