Explain the calculation of radius of tetrahedral void

Q. The radius of void in a closed packed tetrahedral is:

Q. For a tetrahedral void the correct relation between r and R is :
Here
$r\text{is radius of the tetrahedral void}$
$R\text{is radius of the atoms in close packing}$

Q. Calculate the radius of tetrahedral void present in the unit cell of an atom X which crystallizes in fcc unit cell having an edge length $a=50\sqrt{2}pm$

Q. An atom crystallizes in a fcc unit cell having radius of $100\sqrt{2}pm$.
Calculate the distance between the two tetrahedral voids which are formed on a same body diagonal

Q. In the closest packing of atoms A (radius : $r_a$), the radius of atom B that can be fitted into tetrahedral voids is: