Question

A wooden cube of 3cm x 3cm x 3cm is painted red on all six surfaces. This cube is then cut into 27 cubes of 1cm x 1cm x 1cm each. How many of these small cubes have none of their surfaces painted red?

Answer 1

27 small cubes have none of their surfaces painted red

Answer 2

Answer:

27 small cubes have none of their surfaces painted red

Step-by-step explanation:

Step 1:

Given data:

A wooden cube painted in all six surfaces =3 cm x 3 cm x 3 cm

Cube cut into 27 cubes=1 cm x 1 cm x 1 cm

To calculate the how many cubes not painted red

Step 2:

Count the 12 edge lines.

So, 6 x 4 / 2=12

Therefore 12 smaller cubes are painted on 2 edges.

Step 3:

So, leaves the 8 corners of the original cube, painted on 3 surfaces.

Step 4:

1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total