Extra Credit Problem $(4$ pts$.)$: A company is constructing a large rectangular box aquarium for a client. The design details of the aquarium specify that it should ideally have a length of $8$ feet, a width of $2$ feet, and a height of $3$ feet. However, an acceptable construction tolerance for each dimension is $+-3$ inches.

a$.$ Calculate the ideal volume of the aquarium in cubic feet.

b$.$ Using the technique of differentials for several variables, find the approximate change in volume if each dimension includes the extra tolerance of $3$ inch.

c$.$ Determine the actual change in volume with the extra $3$ inch.

d$.$ Calculate the additional weight of water that the aquarium can hold due to the $3-$inch tolerance, using the fact that one cubic foot of water weighs $62\mathrm{.}4$ pounds.

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