How much dirt is there in a 6 feet deep hole and 10 inches in diameter?

Answer 1

None. It's a hole!

If you mean how much volume of dirt was extracted to create that cylindrical hole:

volume = π x radius2 x depth

= π x (10/2 in)2 x 6 ft

= π x (10/2 in)2 x (6 x 12 in)

≈ 5654 cu in

≈ 3.27 cu ft

but note that if the dirt was dug out bit by bit and not extracted as a cylindrical core, the volume of the resultant heap of dirt will have a larger volume as there will be air included in it.