$A$ face-centred cubic $(FCC)$ unit cell is made up of two types of atoms $A$ and $B$,in which $A$ occupies the corner positions and $B$ occupies the face centres. If atoms along one of the body diagonals are removed,what is the empirical formula of the remaining solid?

In hexagonal systems of crystals,a frequently encountered arrangement of atoms is described as a hexagonal prism. Here,the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. $A$ space-filling model of this structure,called hexagonal close-packed $(HCP)$,is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally,the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be $r$.
$1.$ The number of atoms on this $HCP$ unit cell is
$(A)$ $4$ $(B)$ $6$ $(C)$ $12$ $(D)$ $17$
$2.$ The volume of this $HCP$ unit cell is
$(A)$ $24 \sqrt{2} r^3$ $(B)$ $16 \sqrt{2} r^3$
$(C)$ $12 \sqrt{2} r^3$ $(D)$ $\frac{64 r^3}{3 \sqrt{3}}$
$3.$ The empty space in this $HCP$ unit cell is
$(A)$ $74 \%$ $(B)$ $47.6 \%$ $(C)$ $32 \%$ $(D)$ $26 \%$
Give the answer for questions $1, 2$ and $3.$

Assertion : In close packing of spheres,a tetrahedral void is surrounded by four spheres whereas an octahedral void is surrounded by six spheres.
Reason : $A$ tetrahedral void has a tetrahedral shape whereas an octahedral void has an octahedral shape.

$A$ compound of formula $A_2B_3$ has the $hcp$ lattice. Which atom forms the $hcp$ lattice and what fraction of tetrahedral voids is occupied by the other atoms?

Identify the types of voids represented by the structures $I$,$II$,and $III$ in the given image.

What is the number of octahedral and tetrahedral voids present respectively in $0.25 \ mol$ of a substance having $hcp$ structure?