Question

rectangular solid that is 6-cm-by-6 cm-by-6 cm is painted on all six faces. then the solid is cut into cubes that measure 2 cm on each side. how many cubes have only one face painted?

Answer 1

If you check the picture below

the rectangular solid is a 6x6x6, so all sides are equal thus is a cube

is painted on all faces, so the only part that's painted is the faces, ok
then you split it like in the picture, you have all 6 faces painted there,

now, let's say each of those 6 faces are cut in 2cm

how many of those 2cm pieces will each have?   so get that amount for each and sum them up, that's how many of the cubes have one face painted

only the cubes that are part of the face, which was painted, are the ones that have a painted face themselves

keep in mind that each face is a 6x6 rectangle
notice the 2nd picture below

Answer 2

Answer: The answer is six cubes.

Step-by-step explanation:  Given that the dimension of a rectangular solid is 6 cm × 6 cm × 6 cm. It is painted on all six faces and is cut into smaller cubes that measure 2 cm on each side. We are to calculate the number of cubes that have only one face painted.

The volume of the rectangular solid is given by

$V_r=6\times 6\times 6=216~\textup{cm}^3,$

and the volume of each small cube is

$v_c=2^3=8~\textup{cm}^3.$

Therefore, the number of small cubes that are made after cutting the solid will be

$n=\dfrac{V_r}{v_c}=\dfrac{216}{8}=27.$

So, there will be 27 small cubes. On one face of the solid, there will be 9 small cubes, out of which only the middle one is painted on one face.

Since there are six faces, so number of cubes that have only one face painted = 1 × 6 = 6.

Thus, the answer is six.