Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Problem: the dimensions of a rectangular solid are 4 inches, 5 inches, and 12 inches. if a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a. 10: 17, b. 2: 5, c. 5: 16, d. 25: 7, e. 10: 21
e