Ahollow cubical box is 0.30 m on an edge. this box is floating in a lake with one-third of its height beneath the surface. the walls of the box have a negligible thickness. water from a hose is poured into the open top of the box. what is the depth of the water in the box just at the instant that water from the lake begins to pour into the box from the lake?

Given hollow cubical box of side 0.30 m=3 dM
volume V=3^3=27 dm^3 = 27 L

Weight of box
= weight of (fresh) water (1 kg/L) displaced
= V/3 = 9 L of water = 9 kg

When water is filled so that the total weight of water equals the weight of volume of box, the top rim of the box will be at water level.

Remaining volume = 27-9=18L
height of 18L of water when water rushes in
= 18/(3^2) = 2 dm  (=0.2m)