I found a suitable example problem. on page 490 of this book

Calculus: Early Transcendentals - Google Books

It seems a little clearer, now how does it change if we submerge the inclined figure further, such that the top no longer "kisses" the surface?

It would seem to me that if the figure were submerged an additional 4 feet, and our height function, h(x) became y+4, the sec(@) or sin@, whatever we choose our reference to be, would skew that plus 4 height...