A cube of dimensions 100*100*100 is painted with Red, Blue and Black on the adjacent pairs of faces and is cut into smaller cubes of dimension 1*1*1 cm. How many cubes will have two of their faces painted with different colour?
Answers
Given: A cube of dimensions 100*100*100 is painted with Red, Blue and Black on the adjacent pairs of faces and is cut into smaller cubes of dimension 1*1*1 cm.
To find: The number of cubes that will have two of their faces painted with different colours.
Solution:
When a 100*100*100 dimensions cube is divided into smaller cubes of dimension 1*1*1, 1000000 such small cubes are formed. There are 8 corners in a cube and these corners will have three of their surfaces painted with three different colours.
A cube has 12 edges and all the edges will form smaller cubes that have two sides painted with two different colours. Each edge would have 100 cubes. This means that there are a total of 1200 cubes on the edges.
12 × 100 = 1200 cubes
When we subtract the eight corner cubes from the 1200 edge cubes, the number of cubes that have two of their faces painted with different colours is obtained.
1200 - 8 = 1192
Therefore, the number of cubes that will have two of their faces painted with different colours is 1192.