Question 835462
The surface area of a sphere is 
{{{SA[s]=2*pi*R^2=2*pi*4^2=32*pi}}}
The cost for that sphere plating is $30.
So the cost per square inch is {{{C=30/(32*pi)=15/(16*pi)}}}
Now for an $80 job,
{{{80=SA*(15/(16*pi))}}}
{{{SA=(80*16*pi)/15}}}
{{{SA=(16*16*pi)/3}}}
{{{2*pi*R^2=(256*pi)/3}}}
{{{R^2=128/3}}}
{{{R=sqrt(128/3)}}}
Use your calculator to get that to the desired decimal places.