Cecil, if you have figured it out from the previous posts, good. But I thought that I would splain it another way.
The formula that they are referring to is Pythagoreans theorem. Look it up on the web for more answers.
But, I think that there is an easier way.
If you are doing a 1 to 1 drop, imagine a square 10 feet by 10 feet, if it had a 1 to 1 drop from one corner to the other, the bisecting line would cut the square exactly in half. So, knowing that a 10 X 10 square is 100 square feet, half would be 50 feet. This can easily be converted to cubic feet.
In the same way, a 2 to 1 drop would take a 20 X 10 box and cut it in half, so the 200 square feet would be bisected into two 100 square foot sections.
So in your application, if you dig down 7 feet, in a 1 to 1 scenario, it would take 7 horizontal feet to get down 7 vertical feet. (Pythagorenans theorem says that the length of that slope would be 9.89 feet.) A 7 X 7 slope, running 10 feet long would be 7 x 7 x 10 = 490 cubic feet, the half you are removing is 245 cubic feet of dirt.
In the 2 to 1 scenario, it would take 14 horizontal feet to get down 7 vertical feet. (Pythagorean says the slope is 15.65 feet long.) A 14 x 7 x 10 cube = 980 cubic feet, taking out half; you are moving 490 cubic feet of dirt. But the flat bottom portion of the pond will be smaller. (By 7 feet on each side) so you have to calculate in a savings there.
