Question

Let's take a Rubik's cube.

We know that a Rubik's cube is made up of 27 identical smaller cubes which make up one large cube as seen in the picture above.

Let us assume that the one of the small cubes is missing. What will be the packing fraction in this case?

• A. $\frac{1}{27}$
• B. $0$
• C. $1$
• D. $\frac{26}{27}$

Answer 1

The correct option is D

$\frac{26}{27}$

Go back to the formula of packing fraction

Packing fraction = $\frac{Volumeoccupiedinside}{TotalVolumeofunitcell}$

Here, the small cubes are analogous to the particles and the big cube is the unit cell.

Let's take the volume of one small cube to be v.

Then the volume of the bigger cube becomes 27v.

Since one small cube is missing, volume occupied will be 27v - v = 26v

So packing fraction = $\frac{26v}{27v}=\frac{26}{27}$