Let B be a right rectangular prism (box) with edge lengths 1,3 , and 4 , together with its interior. For real r \geq 0, let S(r) be the set of points in 3-dimensional space that lie within a distance r of some point in B. The volume of S(r) can be expressed as a r^{3}+b r^{2}+c r+d, where a, b, c, and d are positive real numbers. What is \dfrac{b c}{a d} ?
Answer Choices
A. 6
B. 19
C. 24
D. 26
E. 38