Question

what is the volume of a regular octahedron inside a cube with the length of its sides measuring 4 centimeters ​

Answer 1

Answer:

We conclude that the volume of a regular octahedron will be:

• $\:\:V\:\approx \:30.17$ cm

Step-by-step explanation:

Given

The length of one of the side or edge of a regular octahedron = a = 4 cm

To determine

The volume of a regular octahedron = V

Using the formula to determine the volume of a regular octahedron

$V\:=\:\frac{\sqrt{2}}{3}a^3$

substituting a = 4 in the volume equation

$V=\frac{\sqrt{2}\cdot \:4^3}{3}$

$V=\frac{64\sqrt{2}}{3}$         ∵ 4³ = 64

$\:\:V\:\approx \:30.17$ cm

Therefore, we conclude that the volume of a regular octahedron will be:

• $\:\:V\:\approx \:30.17$ cm