An engineered titanium dioxide (TiO2\text{TiO}_2TiO2) nanoparticle, used as an inorganic UV filter in high-performance sunscreens, is synthesized in the shape of a square-based nanopillar (a cuboid).
The square base of the nanopillar has a side length of 6 nm6\text{ nm}6 nm, and its height is 24 nm24\text{ nm}24 nm.
a.[2]
Calculate the volume of this titanium dioxide nanoparticle.
b.[2]
Calculate the total surface area of the nanoparticle.
c.[2]
Calculate the surface-area-to-volume ratio of the nanoparticle.