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Examveda

Length of each edge of a regular tetrahedron is 1 cm. It volume is :

A. $$\frac{{\sqrt 3 }}{{12}}{\text{ }}c{m^3}$$

B. $$\frac{1}{4}\sqrt 3 {\text{ }}c{m^3}$$

C. $$\frac{{\sqrt 2 }}{6}{\text{ }}c{m^3}$$

D. $$\frac{1}{{12}}\sqrt 2 {\text{ }}c{m^3}$$

Answer: Option D

Solution(By Examveda Team)

Length of each edge of a regular tetrahedron = 1 cm
Volume of regular tetrahedron :
$$\eqalign{ & = \frac{{{a^3}}}{{6\sqrt 2 }}{\text{ c}}{{\text{m}}^3} \cr & = \frac{1}{{6\sqrt 2 }} \cr & = \frac{{\sqrt 2 }}{{6\sqrt 2 \times \sqrt 2 }}{\text{ c}}{{\text{m}}^3} \cr & = \frac{{\sqrt 2 }}{{12}}{\text{ Or }}\frac{1}{{12}}\sqrt 2 {\text{ c}}{{\text{m}}^3} \cr} $$

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