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cylinder question

 
 
guy101
 
Reply 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
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Type: Discussion • Score: 1 • Views: 463 • Replies: 2
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markr
 
  1  
Reply Thu 18 May, 2006 09:57 pm
multiply by r^2 (understanding that r=0 is not a solution)
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Brandon9000
 
  1  
Reply Tue 23 May, 2006 03:23 pm
This is correct. Just solve for r.
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