4. There are 6 identical rectangular prisms with edge lengths of $3 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$, respectively. Some of their faces are painted red, so that some prisms have only one face painted red, some have exactly two faces painted red, some have exactly three faces painted red, some have exactly four faces painted red, some have exactly five faces painted red, and one prism has all six faces painted red. After painting, all the prisms are divided into small cubes with an edge length of $1 \mathrm{~cm}$. After the division, what is the maximum number of small cubes that have exactly one face painted red?
4. 【Solution】For a cuboid with one face painted red, it is evident that a $4 \times 5$ rectangle should be painted red, which results in 20 small cubes with one red face, the maximum number.

For a cuboid with two faces painted red, it is evident that two $4 \times 5$ rectangles should be painted red, which results in 40 small cubes with one red face, the maximum number.

For a cuboid with three faces painted red, the $4 \times 5$, $4 \times 5$, and $4 \times 3$ faces should be painted red, producing $4 \times (5+5+3-4) = 36$ small cubes with one red face, and any other method results in fewer than 36 such cubes.

For a cuboid with four faces painted red, the $4 \times 5$, $4 \times 5$, $4 \times 3$, and $4 \times 3$ faces should be painted red, producing $4 \times (5+5+3+3-2 \times 4) = 32$ small cubes with one red face, and any other method results in fewer such cubes.

For a cuboid with five faces painted red, only one $3 \times 5$ face should be left unpainted, which results in $(3-2)(5-2) + (4-1)(5+5+3+3-2 \times 4) = 27$ small cubes with one red face, and any other method results in fewer than 27 such cubes.

For a cuboid with six faces painted red, it produces $2[(3-2)(5-2) + (5-2)(4-2) + (4-2)(3-2)] = 22$ small cubes with one red face. 

Thus, the maximum number of small cubes with one red face is $22 + 27 + 32 + 36 + 40 + 20 = 177$.