Question

125 small but identical cubes are put together to form a large cube. this large cube is now painted on all six faces. how many of the smaller cubes have no face painted at all. select one: a. 27 b. 64 c. 36 d. 8

Answer 1

Figure a cube which has 125 small cubes then now you want to paint on all six faces of the cube and find the no paint cubes.

Obviously inside cubes are remain no paint.

So look at the painted cubes that are 9 cubes in row 2, 9 cubes in row 3 and 9 cubes in row 4.  

Thus the total numbers of cubes that have no painted face are 27 (9+9+9).

Answer 2

Find the length of the large cube:

Volume = Length³

Length³ = 125

Length = ∛125

Length = 5

The outer layers are painted, find the number of inner cubes:

Length of inner cube = 5 - 2 = 3

Volume = 3 x 3 x 3 = 27

Answer: 27 of the cubes have no face painted.