Question 990244
{{{v=pi*h*r^2}}}, {{{s=2*pi*r^2+2pi*r*h}}}, and {{{v=170}}}.



s is for surface area of the can.


v formula gives {{{h=v/(pi*r^2)}}}
{{{s=2pi*r^2+2pi*r(v/(pi*r^2))}}}
{{{s=2pi*r^2+2v*pi/(pi*r)}}}
{{{highlight(s=2pi*r^2+2v/r)}}}


Find ds/dr and equate to 0, and solve this for r.


{{{ds/dr=4pi*r+2v(-1)(r^-2)}}}
{{{ds/dr=4pi-2v/r^2=0}}}
{{{highlight_green((4pi*r^2-2v)/r^2=0)}}}



Actually, you are looking for {{{highlight(2pi*r^2-v=0)}}}------Solve this for r.