Hi curious one :)

First I calculated the volume of the space before me, as I stand on the beach looking out at the sea, at a depth of one foot to the horizon.
(I assumed I was on a 100% straight beach.)

Sooooooooo - that would be figuring the volume of a cylinder - actually half a cylinder, because I'm not counting the land behind me.
Half of a pie, etc. And yes, I didn't allow for the curvature of the earth because that stretches my math brain cells a little farther
than they're used to. I think accounting for the earth's curvature would actually make the final number even larger ... if I had to guess. :)

So first, I figured out the volume of this imaginary semi-cylinder:

(pi x height x radius x radius)/2 = half the volume of a cylinder

The radius would be the distance to the horizon. - approx. 2.7 miles or 14,256 ft.

Sooooooo - that would be

(3.14 x 1 foot x 14,256 ft x 14,256 ft)/2 = 319,080,000 cubic feet = the volume to the horizon at 1 ft depth.

And how many gallons are there in a cubic foot? 7.48 gallons

So the volume in gallons to the horizon at a depth of one foot is
319,080,000 cubic feet x 7.48 gallons = 2,386,700,000 gallons

The latest U.S. government's estimates of total oil spilled to date in the Gulf of Mexico, as of June 14, 2010, is anywhere from 48 million to 110 million gallons.
I'm going to use the high estimate because the spill isn't close to containment.

110,000,000 gallons spilled/ 2,386,700,000 gallons in my model = .05

So this means that, if you were standing on an incredibly straight beach and you're 5 ft 10 inches tall - like me, then about 5% of the ocean you see would be 1 ft deep in oil.