Question 891333
v = volume
r = radius
h =length of can or could be consdired as height
S = surface area
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{{{v=pi*r^2*h}}}
{{{S=2*pi*r^2+h*2pi*r}}}


You want S as a function of r, and you know v is a given constant, but h is unknown.  You can use the v equation and solve for h and therefore eliminate h as a variable in the s equation.


{{{h=v/(pi*r^2)}}};
{{{S=2pi*r^2+(v/(pi*r^2))2pi*r}}}
{{{S=2pi*r^2+(2pi*r*v)/r^2}}}

{{{highlight(S=2pi*r^2+2pi*v/r)}}}


The cost of the can is only slightly more complicated.  Track from where each term came.  The top and bottom EACH is {{{pi*r^2}}}.  The circular shaped side is {{{2pi*v/r}}}.


{{{highlight(C=6(2pi*r^2)+4(2pi*v/r))}}}.
Simply substitute your needed values for r, and v, and compute the value for C as cents for the can.