Question

Find the volume $\mathrm{V}$ of a regular tetrahedron whose face is an equilateral triangle of side $8$.

Answer 1

Find the volume of the regular tetrahedron:

Use the regular tetrahedron volume formula $V=\left(\frac{s^3}{6\sqrt{2}}\right)$.

Where, $s$ is the side of the equilateral triangle.

Substitute $s=8$ in above formula:

$\begin{array}{c}\Rightarrow V=\left(\frac{(8{)}^3}{6\sqrt{2}}\right)\\ =\left(\frac{512}{6\sqrt{2}}\right)\\ =\left(\frac{256}{3\sqrt{2}}\right)\\ =\left(\frac{128\sqrt{2}}{3}\right)\\ =60.33977866\\ \approx 60.34\end{array}$

Hence, the volume of the regular tetrahedron whose side $\mathbf{8}$ is $\mathbf{60}\mathbf{.}\mathbf{34}$ cubic units.