Practice | Hashtable

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

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

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

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

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

Solution:

Length of each edge of a regular tetrahedron = 1 cm
Volume of regular tetrahedron :

\begin{aligned} = \frac{a^{3}}{6 \sqrt{2}} c m^{3} \\ = \frac{1}{6 \sqrt{2}} \\ = \frac{\sqrt{2}}{6 \sqrt{2} \times \sqrt{2}} c m^{3} \\ = \frac{\sqrt{2}}{12} Or \frac{1}{12} \sqrt{2} c m^{3} \end{aligned}

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