\(W_{uw} = 64 \frac{lbs}{ft^3}\) is the unit weight of water and \(W_{ui} = 7.2 (640 = 460.8 \frac{lbs}{ft^3}\) is the unit weight of iron.
Weight of tank when empty, \(W_e = W_{ui}Vol_{iron}\)
Weight of tank when full, \(W = W_e + W_(uw)Vol_{water}\)
Calculate the volume of the tank.
\(Vol_{tank} = Vol_{out} - Vol_{in}\)
\(Vol_{out} = (3.5+\frac{1}{6})(\frac{14}{3} +\frac{1}{6})(\frac{13}{3} + \frac{1}{12}) \)
\(Vol_{out} = 78.27\)
\(Vol_{in} = (\frac{14}{3})(3.5)(\frac{13}{3})\)
\(Vol_{in} = 70.78\)
\(Vol_{tank} = 78.27-70.78 = 7.50~ ft^3\)
The volume of water is same volume as the \(Vol_{in}\)
Weight of the tank when empty.
\(W_e = 460.8 (7.50) \)
\(W_e = 3453.87 ~lbs\)
Weight of the tank when full with saltwater.
\(W = 3453.87 + 64 (70.78) = 3453.87 ~lbs\)
\(W = 7983.64 ~lbs\)