$($Conversion$)$ The volume of a sphere can be determined by using this formula:

$V=(\frac{4}{3})r^3$

$V$ is the volume of the sphere.

$$ is the dimensionless number $($no units$)$ having the value $3\mathrm{.}1416,$ accurate to four decimal places.

$r$ is the radius in centimeters $(cm)$ of the sphere.

a$.$ Determine the units of $V$ by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for volume listed in Table $1\mathrm{.}1.$

b$.$ Determine the volume of a sphere having a radius of $8cm.$

c$.$ If you were required to write a computer program to determine the volume of a sphere, what inputs, outputs, and algorithm would you use?