Question

3 the volume of a regular tetrahedron (a pyramid made from 4 equilateral triangles) with side length s is given by the formula ( v=\frac{1}{6sqrt{2}}cdot s^{3} ).
a. solve this equation for s to get the side length in terms of the volume.

Explanation:

Step1: Isolate \(s^{3}\)

Given \(V=\frac{1}{6\sqrt{2}}\cdot s^{3}\), multiply both sides by \(6\sqrt{2}\) to get \(s^{3}=6\sqrt{2}V\).

Step2: Solve for \(s\)

Take the cube - root of both sides. Using the property \(\sqrt[3]{a\cdot b}=\sqrt[3]{a}\cdot\sqrt[3]{b}\), we have \(s = \sqrt[3]{6\sqrt{2}V}\).

Answer:

\(s=\sqrt[3]{6\sqrt{2}V}\)