A small barge is being used to transport trucks across a river. if the barge is 10.00 m long by 8.00 m wide and sinks an additional 3.65 cm into the river when a loaded truck pulls onto it, determine the weight of the truck and load.

Okay, so I suggest to follow the Archimedes Principle ...

Volume of water displaced--> 10.00m * 8.00m * 0.0405m=3.24m^3

Density of water--> 1000kg/m^3

Mass of water displaced = volume x density=3.24x1000=3240kg

Mas of water displaced (mg) = 3240 x 9.81=31800N

Weight of truck + load=31800N