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Thu 18 May, 2006 08:27 pm
The cylinder has a volume of 30m^3
What dimensions will use the least material...
SO we have
V = pi.r^2.h
SA = 2pi.r^2.h + 2pi.r.h
i try to find the surface area in terms of one variable
so i get h = 30 / pi.r^2 and sub in
SA = 2pi.r^2 + 2pi.r.(30/pi.r^2)
i then get...
SA = 2pi.r^2 + 60r^-1
find the first derivative
dSA/dr = 4pi.r - 60r^-2
to find the turning points and thus the minimum find r when dSA/dr = 0
0 = 4pi.r - 60r^-2 and thats where i get stuck. im not even sure if im on the right track, so feel free to shut me down.
sorry for a long question but any help helps.
thanks
multiply by r^2 (understanding that r=0 is not a solution)
This is correct. Just solve for r.