TS EAMCET 5-Aug-2021 Shift 1 Question Paper

Let the edge length of the cube be a and radius of atom be r.
Now, in simple cube,
number of atoms present =1∕8×8=1
So, volume occupied =1×‌

4

3

πr3
Now, in simple cube atoms at corners will be touching each other.
⇒‌‌a=2r⇒r=a∕2
Volume of cube =a3
So, fraction of total volume occupied =‌

‌ 4 3 πr3

a3

=‌

‌ 4 3 ×π×( a 2 )3

a3

=‌

4

3

×π×‌

1

8

=‌

π

6