设该长方体的棱长分别为$$a$$厘米，$$b$$厘米，$$c$$厘米，$$(a\geqslant b\geqslant c)$$，  则由题意得$$(a-2)(b-2)(c-2)=11$$，  ∵$$11$$为质数，  ∴$$a-2=11$$，$$b-2=1$$，$$c-2=1$$，  ∴$$a=13$$，$$b=3$$，$$c=3$$，  ∴长方体的体积$$V=abc=117$$立方厘米． 
将一个棱长是整数厘米的长方体的各表面都刷成红色，然后将这个长方体分割成若干个棱长为$$1$$厘米的小正方体，若任何一面都没有涂色的小正方体有$$11$$个，则原来的长方体的体积是~\uline{~~~~~~~~~~}~立方厘米．  Brush each surface of a box with integral centimeter of edge length into red, and then divide the box into several small cubes with an edge length of $$1$$ cm. If there are $$11$$ cubes without color on any face, the volume of the original box is~\uline{~~~~~~~~~~}~cubic centimeter.
Options:
A. $$117$$ 
B. $$99$$ 
C. $$96$$ 
D. $$84$$ 
E. $$48$$ 