A cubic box with an edge length of 4 inches holds a ball with a
radius of 2 inches, such that the ball touches the box on all
six sides (it is tangent to all six sides). What is the
distance, in inches, between the center of the ball and a corner
of the box? A. 6√3 B. 4√3 C. 2√3 D. 2√2 E. √2 (C) The distance
between the center of the ball and any of the 8 corners of the
cube is simply one-half the distance between two of the opposite
corners of the cube. To imagine opposite corners in a cube, pick
any corner, and think about drawing a line through the center of
the cube to the furthest other corner. The distance between any
two opposite corners in a 3 dimensional rectangular solid
(whether a perfect cube or not) can be determined very quickly
using the 3 Dimensional Pythagorean theorem: D² = a² + b² + c²,
where a, b, and c represent the dimensions of the solid. Since
all of the edge lengths of a cube are the same, we can simplify
the equation to: D² = 3a², where a represents the edge length of
the cube. So th