The volume of this hcp unit cell is:

24 \sqrt{2} r^{3}

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16 \sqrt{2} r^{3}

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12 \sqrt{2} r^{3}

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\frac{64}{3 \sqrt{3} r^{3}}

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Solution

The correct option is C $24 \sqrt{2} r^{3}$
Volume = area of base $\times$ height
Area of base $= 6 \sqrt{3} \times r^{2}$
Height of unit cell $= \sqrt{\frac{2}{3}} 4 r$
Volume $= 6 \sqrt{3} \times r^{2} \times \sqrt{\frac{2}{3}} 4 r = 24 \sqrt{2} r^{3}$

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