A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.0 m long, 2.2 m wide, and 2.3 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloon's radius is 1.7 m, the shipping container just begins to rise towards the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3.

Answer 1

I am not sure I have ever seen a really watertight shipping container but anyway:)

Volume of container = 6*2.2*2.3 = 30.36 m^3
Buoyancy of container = 30.36*1025 g N = 31,119 g N

Buoyancy of lift bag = 1025 g (4/3) pi r^3 = 21,094 g N

total up force = 52,213 g N

total down force = mass of container * g

so
mass of container = 52,213 kg

Answer 2

I used another method of solving this problem. I also tried using your method and let me tell you that it really worked.