Show that if a unit cube can be rounded off using ruler and compasses only, then r= $(3/2\pi)^{1/2}$ is constructible.
Show that $r$ is transcendental over $\mathbb Q$
I am not that familiar with rounding off cubes to show that $r$ is constructible any pointers in showing how we get to $r$
I don't know what "rounded off" means either, but to complete this problem, you don't need to know. All you need to know is that the first statement is true, namely, that if that operation is possible, then $r = \sqrt{\frac{3}{2\pi}}$ is constructable.
By showing $r$ is transcendental over $\Bbb Q$, you then know that $r$ is not constructable, hence that a cube cannot be "rounded off" (whatever that may mean).