How Much Did the Hungry Worm Eat?

Last Problem:

Is it legal for a man to marry his widow’s sister?
Answer: The man is dead if he has a widow, so
he is not in any position to marry anyone!


Today’s Problem:

A hungry, exotic, four inch worm loves
to eat paper for a special treat. This
particular worm discovers by chance a
full set of 1964 Collier’s encyclopedias
sitting on the bottom self of Professor
Moriarty’s book shelf on Daft Street in
London on a sunny day in November.

The worm starts eating from the front
cover of the first volume. He eats all the
way through to the back of the back cover
of the third volume before being discovered
by Professor Moriarty who was investigating
the etiology of Asian worms that are longer
than one inch long.

If the covers of each book are each 1/2 cm
think and the pages of each volume are 8 cm
think, how many centimeters did the worm eat
before he was discovered by Professor Moriarty?