In an $fcc$ arrangement of $A$ and $B$ atoms, $A$ atoms are at the corners of the unit cell and $B$ atoms are at the face centers. If one of the $A$ atoms is missing from one corner, what is the simplest formula of the compound?

What is the formula for packing efficiency?

Calculate the void volume in an $fcc$ unit cell if the total volume of the unit cell is $6.4 \times 10^{-23} \text{ cm}^3$.

What is the percentage of unoccupied volume in $BCC$ structure (in $\%$)?

Explain three-dimensional close packing from two-dimensional hexagonal close packing. Explain the formation of face-centered cubic $(FCC)$ unit cell and hexagonal close packing $(HCP)$ in three dimensions.

$A$ two-dimensional solid is made by alternating circles with radius $a$ and $b$ such that the sides of the circles touch. The packing fraction is defined as the ratio of the area under the circles to the area under the rectangle with sides of length $x$ and $y$. The ratio $r=b/a$ for which the packing fraction is minimised is closest to $.....$