{"status": "success", "data": {"description_md": "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 $h$?\n\n
\n
\n\n$\\textbf{(A) }2+2\\sqrt 7\\qquad\\textbf{(B) }3+2\\sqrt 5\\qquad\\textbf{(C) }4+2\\sqrt 7\\qquad\\textbf{(D) }4\\sqrt 5\\qquad\\textbf{(E) }4\\sqrt 7\\qquad$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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?


\\textbf{(A) }2+2\\sqrt 7\\qquad\\textbf{(B) }3+2\\sqrt 5\\qquad\\textbf{(C) }4+2\\sqrt 7\\qquad\\textbf{(D) }4\\sqrt 5\\qquad\\textbf{(E) }4\\sqrt 7\\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p18", "prev": "/problem/14_amc12A_p16"}}