# Chapter 3 - The Structure of Crystalline Solids - Questions and Problems - Page 97: 3.6

The proof is below.

#### Work Step by Step

$APF=\text{{volume of atomic unit cell}}/{\text{total unit cell volume}}$ $V_{s}=\frac{4}{3}\pi r^3$ HCP has total 6 atoms, so the total volume is: $V_{s}=6\times\frac{4}{3}\pi r^3=\frac{24}{3}\pi r^3$ For HCP, ${r}=$$\frac{a}{2}$ $V_{c}=6r^2c\sqrt{3}$ where $\frac{c}{a}=1.633$ $V_{c}=6\times3.266{\sqrt{3}}r^3$ APF =$\frac{\frac{24}{3}\pi r^3}{6\times3.266{\sqrt{3}}r^3}=0.74$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.