Yes, “a huge amount of work” is grammatically correct and perfectly acceptable phraseology. As a general measure of quantity, “amount” is practically synonymous with “volume” for indicating the total of a thing or things in number, size, value, or extent. Indeed, the sense of “a huge amount of work” is in general almost indistinguishable from that of “a huge volume of work”
However, when it comes to describing specific kinds of work, there’s a difference in nuance between “amount” and “volume.” In particular, lots of work of an abstract nature such as reading, thinking, or surveillance is more precisely described as “a large amount of work,” while lots of measurable physical work like loading a pile of boulders into a truck is more precisely described as “a large volume of work.” Some dissonance might be perceived if lots of abstract work is described as “a large volume of work” instead, but no such dissonance will be perceived if lots of physical work is described as “a large amount of work” instead. The differences will be largely subjective, with different writers or speakers gravitating to either “amount” or “volume” as a matter of temperament or personal style. Either way, it will be needless or foolhardy to fault them for their choice of usage.
