Hello Aspirant!

I'll show you the derivation in short to calculate the packing efficiency of a scc.

Let the length of side of the simple cubic cell (scc) be 'a', and the radius of each atom be 'r'.
So, a =2 x r
Volume of cube = a^3
=(2r)^3
=8r^3

In a simple cubic unit cell, there is only one spherical atom,
=> volume of a sphere = 4/3 x x r^3

Since, Packing efficiency
= (Volume of the cube/Volume of a sphere)
100%
Therefore, packing efficiency of a simple cubic unit cell = (8r^3 / (4/3) x r^3) x 100
= 52.4%.

Here, r^3 means 'r raised to the power 3' or 'r cube'.

Hope you are able to understand.