1 acre is 6,272,640 square inches and you want half an inch in volume so we can just divide the area by half for 3,136,320 then convert to gallons which turns out to 13,577.14 and if you round up you get 14,000 gallons.
That checks out.. I don't think whether in the top 10 inches or down to bedrock matters if you are calculating volume at 1771 x 1771 x 0.5 since it is only for half an inch across the whole acre....
wait a minute....lets do the math with cubic acres instead of square acres..
So to get how many cubic inches are in a square acre you get the square root of 6,272,640 and cube it to get: 15,709,976,839 so that is the volume of an acre in cubic inches. 5% of that is 785498842 cubic inches or 3,400,427 gallons. The total height is 2504 cubic inches but we are only interested in the top 10 inches.
Screw it, its late I'm tired so I googled a "topsoil calculator" and 1/2inch on an acre is 2 cubic feet which in gallons is 14.96104 rounded to 15 gallons. How this magic calculator gets to that math I have no idea, I would probably figure it out eventually but area to volume conversions hurt my brain.
15 gallons of biochar.. yay
But if you ordered 14,000 gallons before you saw this...send pics. XD