Question

Volume of HCP unit cell is :

• A. 24$\sqrt { 2 }$r3
• B. 8$\sqrt { 2 }$r3
• C. 16$\sqrt { 2 }$r3
• D. 24$\sqrt { 3 }$r3

Answer 1

Answer: (A)

24$\sqrt { 2 }$r3

Answer 2

Volume of hexagon :

tan30⁰ = $\frac{a}{2 \times y}$ So y = $\frac{a \times \sqrt{3}}{2 \times 1}$ = $\frac{\sqrt{3}}{2}$a 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

= $\frac{6\sqrt{3}}{4}$ × a2 × 2$\sqrt{\frac{2}{3}}$ a = $\frac{6\sqrt{3}}{4}$ × (2r)2 + 2 $\sqrt{\frac{2}{3}}$× (2r)

= 24 $\sqrt { 2 }$ r3