Atoms A,B,C and D are present at edge centres, body-centre, corners and face-centres respectively. If the atoms present at (or touching ) the surface of a sphere (just inside the cubic unit cell) are removed then what is the formula of the compound ?

Explanation

To solve the problem, we need to analyze the contributions of the atoms A, B, C, and D in the cubic unit cell and determine which atoms remain after removing those that are present at or touching the surface of a sphere just inside the cubic unit cell.

### Step-by-Step Solution:

1. **Identify Atom Positions and Contributions**:
- Atom A is located at the edge centers. Each edge of the cube has one atom A, and since there are 12 edges in a cube, the contribution of A in the unit cell is:
\[
\text{Contribution of A} = 12 \times \frac{1}{4} = 3
...