Question

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

Answer 1

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

• 
  `\:\:V\:\approx \:30.17` cm

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\:=\:(√(2))/(3)a^3`

substituting a = 4 in the volume equation

`V=(√(2)\cdot \:4^3)/(3)`

`V=(64√(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