The bookworm nibbles his way through approximately eight inches.

A set of books on a shelf will have the first book on the left and the first page of the first volume is the rightmost page of the first volume.

Similarly the last page of the last volume is the leftmost page of the last volume.

So the only part of the first volume he eats is the front cover, and the only part of the last volume he eats is the back cover.

The reason the answer is not fourteen inches is that while each leaf is .01 inches thick, each leaf is two pages. So 400 pages is only two inches thick.

Finally, we say approximately eight inches because it is a matter of semantics whether the bookworm ate the first page of the first volume.