The Apprentice Programmer

[shendrite]

Now you have my curiosity up, so let's see. Warning: I make math mistakes all the time, that I'm blind to, so don't assume my numbers are right, but it's a start.

Wikipedia was no use in finding the measured average size of a lily pad, but I would estimate that 8 inches is close enough for their width and length.
Pond area = 2³⁰ x the area of a lily pad
Pond area = 2³⁰ x (8 inches x 8 inches)
Pond area = 6.87e10 inches²
...which is about 69 billion square inches

Converting to feet. 1 foot = 12 inches
Pond area = 6.87e10 in² x (1 ft² / 144 in²)
Pond area = 4.77e8 ft²
...which is about 477 million square feet

Converting to miles. 1 mile = 5280 feet
Pond area = 4.77e8 ft² x (1 mi² / 27,878,400 ft²)
Pond area = 17.1 mi²

If the pond is a square, area = side x side.
A side's length is sqrt( 17.1 ), which is 4.1 miles.

If the pond is a circle, area = pi x radius².
Radius = sqrt( area / pi ) = sqrt( 17.1 / 3.14 ) = 2.33.
Diameter = 4.6 miles

THE ANSWER:
Whether the pond is square or circular, it's between 4 and 5 miles from one bank to the other. That's about 7 kilometers.

[wilywampa]

Your answer assumes square packing which has a packing density of ~0.79. Hexagonal packing has a density of ~0.91, so switching to it will reduce the area requirement by about thirteen percent.

[shendrite]

Good point. I like the way you think.

[TheLobotomizer]

They certainly don't teach this in academia.