Question

Three different faces of a cube are painted in three different colours–red, green and blue. This cube is now cut into 216 smaller but identical cubes. What are the least and the largest numbers of small cubes that have exactly one face painted?

Answer 1

Step 1:

Let us consider a cube having each side of 6 cm then it's volume will be 216 cm^3

If we cut 226 cubes from it then each cube will be 1 x 1 x 1

Step 2:

16 x 6=96 will have one side colored

8 cubes have three sides colored

4 x 4 x 4 =64 are not colored  

Step 3:

4 on each edge has two sides colored so on 12 edges total with

Two sides colored 4 x 22=48

Step 4:

So total=96+8+64+48=216

Answer 2

Concept

A cube is a 3 dimensional figure having 6 sides,6 vertex.

Given

Three colours are painted on the cube and 216 cubes are cut.

Explanation

Suppose the side of cube is 6 cm then its volume will be 216 cm cube.

If we cut 216  cubes then each cube will be 1*1*1

16*6=96 will have one side coloured, 8 cubes  have three sides  coloured and 4*4*4=64 are not coloured.

4 on each edge has two sides coloured so on 12 edges total with two sides coloured 4*22=48

So total =96+8+64+48=216.

Hence maximum 216 number of small cubes have only face painted.

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