Question

b. if the volume of a regular tetrahedron is 18√2 cubic centimeters, what is the length of one of the sides of the tetrahedron?

Explanation:

Step1: Recall the volume formula for a regular tetrahedron

The volume formula for a regular tetrahedron with side length \(a\) is \(V=\frac{\sqrt{2}}{12}a^{3}\).

Step2: Substitute the given volume into the formula

We are given \(V = 18\sqrt{2}\), so \(\frac{\sqrt{2}}{12}a^{3}=18\sqrt{2}\).

Step3: Solve for \(a\)

First, divide both sides of the equation by \(\sqrt{2}\):
\(\frac{1}{12}a^{3}=18\).
Then multiply both sides by \(12\):
\(a^{3}=18\times12 = 216\).
Take the cube - root of both sides:
\(a=\sqrt[3]{216}\).

Answer:

\(a = 6\) centimeters.