Nice work. =)
When the peak of the iceberg points down, the underwater
part and the entire iceberg have the same shape.
Let h be the height of the iceberg.
Proportions in objects of the same shape are the same,
except that they are squared for areas and cubed for volumes,
((h-1) : h)^3 = 9 : 10
from which h = 1 ft / (1 - (9 : 10)^(1/3)) , or about 29 feet.
When the iceberg keels over, the part above water is of
the same shape as the entire iceberg, with volume ratios
1 : 10. Let x be the height of the visible part of the iceberg.
(x : h)^3 = 1 : 10
x = (1 : 10)^(1/3) h
x = 1 ft * (1 : 10)^(1/3) / (1 - (9 : 10)^(1/3))
which is about 13 ft.