Question 715053
a soup can is tol hold 600 mL of soup. Determine the dimensions of the can with minimum surface area
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{{{Vol = pi*r^2*h}}}
--> {{{h = Vol/(pi*r^2)

{{{SA = 2pi*r^2 + 2pi*r*h}}} (2 ends and the lateral surface)
sub for h
{{{SA = 2pi*r^2 + 2*Vol/r}}}
{{{dSA/dr = 4pir - 2*Vol/r^2 = 0}}}
{{{2*pi*r = Vol/r^2}}}
{{{Vol = 2*pi*r^3}}}
{{{r = root(3,(600/(2pi)))}}}
r =4.57078 cm
h = 9.1456 (= 2r)