Depth of box floating in water using density...?

Question

A rectangular box: Density=625Kg/m(cubed)
                           [4m (wide) x 8m (tall) x 25m (long)]
                           Mass=500,000Kg
Given: Density of water=1000Kg/m(cubed)

Now, how deep will the box sink in water?!?!
I know it is still partially above water (b/c it is less dense than water), but how deep is the section that is submerged?

Trevor H · Accepted Answer

This is a Archimedes principle problem.
 The box will displace its own mass of water = 500,000kg, or 500m³
 Volume of box = 4*8*25 = 800m³
It will sink down to displace 500m³ and 300m³ will remain above the water. What is the height?
 300 = 4*25*H
H = 300/100
H = 3 metres.
Answer: 3 metres of the box will be above the water. 

You can also do this in one step:
 8*0.625 = 5 
5 metres will sink, 3 metres above water.

Depth of box floating in water using density...?

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