Fern:
I think the 12 in your formula should be a 4. If you assume the hole you dig is a cylinder of height h and diameter h, then the horizontal cross-sectional area is <pi>(h/2)^2 and the volume of the hole is V=<pi>(h/2)^2*h=<pi>(h^3)/4. This implies that h=(4V/<pi> ^(1/3), so to estimate the depth of a hole from the volume, you would take V, multiply by 4, divide by pi, and take the cube root of the result. This would give you the depth of a cylindrical hole of volume V with height equal to diameter. Perhaps you used a different assumption?