Minimum Distance between surface of sphere and cube

[CmlDexter]

Homework Statement

Find the minimum distance between the surface of a sphere with radius 3 with center (2,1,2) and a cube with length 6 with center (12,11,12)

Homework Equations

sphere formula: (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2

The Attempt at a Solution

Don't know how to attempt this problem. My assumption is to find the distance between the two centers, then subtract the distance between the radius and the surface of the sphere, and also subtract the distance between the center of the cube to one of the sides. would this procedure be correct?

 

[CornMuffin]

Your procedure is partially correct... but you will want to find the minimum distance between the center of the sphere and a point on the cube. (not the distance between the centers)
then you will just subtract the radius from that number