Transmute Rock to Sand, and Transmute Rock to Mud are both fourth level spells that have a caveat stating they can only affect up to a depth of 10 ft from the surface they are cast on. Does this need to be a flat, 10-ft square on one side of the cube to be affected, or can it take another shape? Likewise, could the surface exist within the cube to be affected? Such as targeting both walls of a one foot passageway to take 5 ft of stone off the left side and 4 ft off the right side?
The specific use case I was imagining would be to have a trained badger, wearing adamantine claw extenders (or an effigy of a badger with adamantine claws) dig a pilot hole that is at least 1.6 ft wide. Because a circle with a radius of 1.6 ft has a circumference of 10 ft, I was wondering if it would be possible to cast the spell on the stone the pilot hole has been dug through, affecting the rest of the 10-ft cube of stone.
The end goal would be to use this fourth level spell to facilitate carving large passages through stony earth with relative ease. Other issues such as sapping, dealing with water sources that could flood the entire tunnel as soon as the stone is transmuted, and the inevitable random encounters, can all be disregarded for this question. What I'm most concerned about is the viability of using the spell in this fashion.