Nice work. =)

SOLUTION

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,

which gives

((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

from which

x = (1 : 10)^(1/3) h

x = 1 ft * (1 : 10)^(1/3) / (1 - (9 : 10)^(1/3))

which is about 13 ft.