Question 824931
Once the block is cut into smaller cubes with 2-inch sides,
but before those cubes get separated,
the original cube looks like this:
{{{drawing(400,400,-1,7,-1,7,
rectangle(0,0,4,4),
green(line(1,0,1,4)),green(line(2,0,2,4)),green(line(3,0,3,4)),
green(line(0,1,4,1)),green(line(0,2,4,2)),green(line(0,3,4,3)),
line(4,4,6,6),line(4,0,6,2),line(0,4,2,6),
line(2,6,6,6),line(6,6,6,2),
green(line(1,4,3,6)),green(line(2,4,4,6)),green(line(3,4,5,6)),
green(line(0.5,4.5,4.5,4.5)),green(line(1,5,5,5)),green(line(1.5,5.5,5.5,5.5)),
green(line(4.5,0.5,4.5,4.5)),green(line(5,1,5,5)),green(line(5.5,1.5,5.5,5.5)),
green(line(4,1,6,3)),green(line(4,2,6,4)),green(line(4,3,6,5))
)}}} It has been cut into {{{4*4*4=4^3=64}}} smaller cubes.
 
Each face of the original cube looks like this:
{{{drawing(300,300,-1,5,-1,5,
rectangle(0,0,4,4),
green(line(1,0,1,4)),green(line(2,0,2,4)),green(line(3,0,3,4)),
green(line(0,1,4,1)),green(line(0,2,4,2)),green(line(0,3,4,3))
)}}} .
On each face of the original cube there are {{{4}}} small cubes, in the middle, that can only get wet on one face. The other cubes around the edges could get wet on more than one face. The edges of each face include {{{red(1)}}} small cube at each corner, and an additional {{{green(2)}}} cubes, in the middle of each edge, that are not at the corners.
 
Parts of the original cube are wet from the rain.
What parts? How many faces, edges, and corners?
Of the 6 faces of the original large cube, {{{5}}} are wet.
Each of the {{{8}}} corners of the original large cube is wet on at least 2 of the 3 faces that make up that corner.
Of the 12 edges, of the original large cube, the 4 edges at the bottom are not wet wet on the bottom side, while the remaining {{{12-4=8}}} edges are wet on both sides.
 
What small cubes are wet on more than one face?
The {{{8}}} cubes at the corners and another {{{2}}} cubes on each of the {{{8}}} edges wet on both sides.
Those add up to
{{{8*red(1)+8*green(2)=8+16=24}}} .
Those small cubes wet on more than one face are {{{24}}} of the {{{64}}} small cubes.
As a fraction/ratio, that is {{{24/64=3*8/(8*8)=3*cross(8)/(8*cross(8))=highlight(3/8)}}}