What is the volume of the octahedron inside this 8m^3 cube?

Question

Answer 1

Side of cube=s=8m
Diagonal of octehedron=d=8m
radius of octahedron=r=d/2=4m
Length of edge of octahedron=a=r*root2=4*root2
Vol. of octahedron=[Root of 2*(a)^3]/3
=[Root of 2*(4 root2)^3]/3
=256/3
Ans is 256/3 m^3

Answer 2

Given a cube of 8 m3, the side of the cube is 2 m.
The octahedron is made up of two(2) cuadrangular pyramides
The volume of a pyramide is calculated as follows: ( area of base x heigth) / 3
Then, the side of the base is Sqrt 2 and height 1
Area of base equals : (sqrt 2)^2 =2
Volume of pyramide : ( 2 x 1) / 3
Volume of two pyramides = volume of octahedron : 2 X 2/3 = 4/3 m3
The answer is 4/3 m3