Pirates of the Caribbean question! (and buoyancy)?

Question

A hollow TREASURE CHEST is 0.40 m on an edge. The TREASURE CHEST is floating in a lake with one third of its height above the surface and the walls of the TREASURE CHEST have negligible thickness and water is poured in. What is the depth of the water in the TREASURE CHEST at the instant that the box begins to sink...

Everything piratey is "in" these days....of course replacing an every day box with a treasure chest will motivate people to help me solve this problem....

thanks for any help

Thanks for any help that you can offer :)

Don't randomly guess unless you know the answer....but the options are
a)0.15m
b) 0.20m
c) 0.27m
d) 0.10m
e) 0.30 m

Answer 1

well that depends on how much Treasure is in it.

Answer 2

if the box has no contents its mass is equal to the mass of a volume of water equal to 2/3 of the boxes volume (it's displacement). so to bring the mass equal to neutral boyancy, add the mass of water equal to 1/3 of the boxes volume.
so fill the box 1/3 full
1/3 of .4 is .133, closest to a, .15

Answer 3

If it is made of wood it would not sink, more likely to capsize making the bottem float on top.