Question

Consider a cube 1 of Cubic Body-Centered unit cell of edge length a. Now atom at the body center at the body center can be viewed to be lying on the corner of another cube 2. Find the volume common to cube 1 and cube 2.

• A. $\frac{a^3}{27}$
• B. $\frac{a^3}{64}$
• C. $\frac{a^3}{2\sqrt{2}}$
• D. $\frac{a^3}{8}$

Answer 1

The correct option is D $\frac{a^3}{8}$

Given edge length of cube $=a$

The common volume is a cube of edge length $\left(a/2\right)$

So, common volume $={\left(\frac{a}{2}\right)}^3=\frac{a^3}{8}$