A researcher synthesizes cubic zinc oxide (ZnO\text{ZnO}ZnO) nanoparticles for use in high-efficiency UV-blocking coatings. The diagram below represents one of these cubic nanoparticles:
The volume of this cubic nanoparticle is 27 nm327\text{ nm}^327 nm3.
Calculate:
a.[2]
The total surface area of the cubic nanoparticle, using the equation: surface area=6×surface area of one face\text{surface area} = 6 \times \text{surface area of one face}surface area=6×surface area of one face
b.[2]
The simplest whole-number ratio of surface area:volume\text{surface area} : \text{volume}surface area:volume for this cubic nanoparticle, written in the form X:1X : 1X:1.