How many small cubes must you add to complete the outlined big cube?

A. 18
B. 30
C. 36
D. 46
E. 52
F. 64

Choose the correct answer.

Question

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Answer :

yugali yugali · Answer 1 · 2023-10-01T23:50:09-04:00

24 out of the 64 small cubes have exactly one painted face.

There are 80 small cubes that have exactly one painted face.

Total number of faces on the big cube:

The big cube has 6 sides, and each side acts as a face.

So, there are 6 faces in total.

Number of small cubes per face:

If you imagine peeling off one face of the big cube, you'll see it's made up of 4 rows of 4 small cubes each.

Therefore, each face consists of 4 x 4 = 16 small cubes.

Cubes with one painted face:

Not all the small cubes on the faces will have just one painted side. Cubes along the edges of the big cube will have two painted sides.

So, we only need to count the cubes that are not on the edges.

Inner cubes on each face:

On each face, there are (4 - 2) = 2 cubes that are not on the edges in each row, both horizontally and vertically.

So, there are 2 x 2 = 4 inner cubes per face that have only one painted side.

Total number of cubes with one painted face:

Since there are 6 faces, and each face has 4 inner cubes with one painted side, the total number is 6 faces * 4 cubes/face = 24 cubes.

Therefore, 24 out of the 64 small cubes have exactly one painted face.

Question

A big cube is made up of 64 small cubes. All the faces of the big cube are then painted. How many of the small cubes have exactly one painted face?