Puzzle Time - Ice Cube edition

[jon-nyc]

Consider a large iceberg that’s a perfect cube. Thanks to the difference in densities between ice and water, 10 percent of the iceberg’s mass is above sea level, while the remaining 90 percent of the mass is below.

In its “optimal” (i.e., lowest-energy) orientation, the iceberg’s center of mass is as deep in the water as possible. Suppose the highest point (or points) of the iceberg is a distance x above sea level, while the lowest point (or points) of the iceberg is a distance y below sea level. What is the ratio of x to y?

[Horace]

I would assume the part above the water would by a symmetric three sided pyramid which contained 10% of the volume of the cube. Then I'd do the math.

[jon-nyc]

Uh, yeah.

[Horace]

The math part doesn't appear to be particularly interesting. Maybe I'm missing something.

[Klaus]

@Horace said in Puzzle Time - Ice Cube edition:

The math part doesn't appear to be particularly interesting. Maybe I'm missing something.

+1

[jon-nyc]

Tough crowd here.

The extra credit version:

What if the ice ‘cube’ is a sphere?