Aspect Ratio and Specific Surface Area: Consider a cube of side a

with the same volume as a sphere of radius $r.$

Show that the surface area of the cube is $1\mathrm{.}24$ times greater

than the surface area of the sphere.

What happens to the surface area $($A$)$ when the size of the sphere

goes from $R$ to $2R?$

What happens to the volume $($V$)$ when the size of the sphere goes

from R to $2R?$

What happens to the surface area$-$to$-$volume ratio $($A$/$V$)$ when the

size of the sphere goes from $R$ to $2$R$?$

What does it mean to say that a circle has an "aspect ratio" of $1?$

Calculate the area$-$to$-$volume ratio of the following shaped nuclei:

A$/$V

A sphere of radius $R,$ with area $4R^2$ and volume $(\frac{4}{3})R^3$

A cube of side $A,$ with area $6A^2$ and volume $A^3$

A cylinder of radius $R$ and height $H,$ with area $(2R^2+2RH)$ and

volume $R^{2}H$

A rectangular parallelepiped of sides A$,$ B$,$ and C$,$ with area $(2$AB $+$

$2BC+2AC$ and volume ABC

Which is easier to nucleate, a sphere or a cylinder? Why?

What do you think is the most important finding in this study

$(3-4$ complete sentences$)?$