What is the volume of the cube if the diagonal is 1?

To find the volume of the cube we need to find the length
of the side.

Given the diagonal of the cube is
1.

Let the side of the cube be
x.

Then we know that the diagonal is given
by:

d = sqrt(3x^2) =
(sqrt3)*x

==> 1=
sqrt3*x

==> x=  1/
sqrt3

==> x=
sqrt3/3

Now we will calculate the volume of
the cube.

We know that the volume of the cube =
x^3

==> V = (sqrt3/3)^3 = 3sqrt3/ 27 =
sqrt3/9

Then, the volume of the cube is
sqrt3/ 9 cubic units.