Question

A pair of opposite faces of a cube is painted yellow another pair of opposite faces orange and the remaining faces white. The cube is then cut in to 125 smaller but identical cubes. How many of the smaller cubes have at most two colours on them?119129117127

Answer 1

Answer:

117

Step-by-step explanation:

The only small cubes with more than two colours are the corner cubes that each get 3 colours.  As there are 8 corners, the number of small cubes with at most 2 colours is then:

125 - 8 = 117

Answer 2

Given: A pair of opposite faces of a cube is painted yellow another pair of opposite faces orange and the remaining faces white. The cube is then cut in to 125 smaller but identical cubes.

To find: How many of the smaller cubes have at most two colours on them.

Solution:

When the cube is divided into smaller cubes, the volume of the larger cube is divided into the volume of 125 smaller cubes. This means that the larger cube is divided into 5 rows and columns each.

$cube_{small} = \sqrt[3]{125}$

               $= 5$

The above calculation is done because the volume of a cube is the cube of its side. Now, the corner pieces will have two colours. So, the number of corner pieces is

$12*5=60$

There are 16 pieces on the surface of the larger cube apart from the corner pieces. The pieces on the surface of the cube will have one colour and so, the number of pieces on the surface excluding the corner pieces is calculated as follows.

$16*6=96$

So, the total number of smaller cubes that have at most two colours is

$96+60=156$

Therefore, 156 of the smaller cubes have at most two colours on them.