Question

Volume of HCP unit cell is :

• A. $24\sqrt{2}r^{3}$
• B. $8\sqrt{2}r^{3}$
• C. $16\sqrt{2}r^{3}$
• D. $24\sqrt{3}r^{3}$

Answer 1

Answer: (A)

$24\sqrt{2}r^{3}$

Answer 2

Volume of hexagon :

$\tan 30^{0} = \frac{a}{2 \times y}soy = \frac{a \times \sqrt{3}}{2 \times 1} = \frac{\sqrt{3}}{2}$ and

Area of hexagonal surface $= 6\left\lbrack \frac{1a}{2} \times \frac{\sqrt{3}a}{2} \right\rbrack = \frac{6\sqrt{3}a^{2}}{4}$

volume of hexagon = area of base × height

$= \frac{6\sqrt{3}}{4} \times a^{2} \times 2\sqrt{\frac{2}{3}a = \frac{6.\sqrt{3}}{4}} \times (2r)^{2} + 24\sqrt{2}r^{3}$