A 4 \times 4 \times h rectangular box contains a sphere of radius 2 and eight smaller spheres of radius 1 . The smaller spheres are each tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. What is h ?
Answer Choices
A. 2+2 \sqrt{7}
B. 3+2 \sqrt{5}
C. 4+2 \sqrt{7}
D. 4 \sqrt{5}
E. 4 \sqrt{7}