Question

find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.

Answer 1

Hint: a "regular hexahedron" is a cube.

Answer 2

hexahedron = volume with six faces.
regular = the six faces are the same.

The volume of a cube is (side)^3

The diagonal of a face is the hypotenuse of a isosceles right-angle triangle.

By Pythagorean theorem:

(hypotenuse)^2 = (side)^2 + (side)^2 = 2*(side)^2
(we know all sides of a cube are the same value)

(side)^2 = (1/2) * (hypotenuse)^2

(don't forget to square the diagonal before dividing by two)

You are given the hypotenuse. Find the value for one side.
Then cube that to find the volume.

Answer 3

And Let me know your answer?

Answer 4

@enolreg