Distance a worm bores across two shelved volumes

Volumes one and two of a book stand next to each other on a shelf in the usual order, spines facing out. In each volume the block of pages is $2$ cm thick and each cover is $2$ mm thick. A worm chews in a straight line from page one of volume one through to the final page of volume two. What distance does it cover?

$4$ mm. With volume one on the left and spines out, its first page sits against its right-hand cover, and volume two's last page sits against its left-hand cover. The worm only passes through those two covers, $2+2$ mm.