Please help with the below Physics Problem?

Question

A wooden cube "just floats" inside water when a 200gm mass is placed on it. When the mass is removed the cube is 2cm above the water level. The side of the cube is_____cm.

I know the answer is 10cm, But please show the process (along with explanation)

Answer 1

Let length of one edge = x
Vol. of cube = L*B*W
Vol. of cube = x*x*x
Vol. of cube = x^3
Vol. of cube = Area * height.
Vol. of cube = x² * 2
Vol. of cube = 2x² cm^3
200 mg = 2x²
x² = 200 mg / 2
x = | ± √100 |
x = 10 cm

Answer 2

When 200 gm is placed 2 A cc of volume of water is displaced where A is the area of the bottom square surface.

The mass of 2A volume of water must also be equal to 200 gm whose volume we know equal to 200cc.

That is 2A = 200 cc
A = 100 cm^2
Since it is a square side is √ 100 = 10 cm.

Answer 3

The amount of water displaced by 2x² cc is equal to 200 gm. Since water has a density of 1 gm/cc there must be 200 cc of water displaced, so
2x² = 200
x² = 100
x = 10 (since -10 doesn't make any sense ☺)

Doug