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Question Number 141368 by bemath last updated on 18/May/21

A closed cylindrical can be is to hold  1 liters of liquid . How should we   choose the height and radius   to minimize the amount of  material needed to manufacture  the can ?

Aclosedcylindricalcanbeistohold1litersofliquid.Howshouldwechoosetheheightandradiustominimizetheamountofmaterialneededtomanufacturethecan?

Answered by TheSupreme last updated on 18/May/21

you have to minimize  S=2πR^2 +πRH  under the constrain  V=πR^2 H=1lt  H=(V/(πR^2 ))  S=2πR^2 +(V/R)  min(S)  (∂S/∂R)=4πR−(V/R^2 )=0 → R=^3 (√(V/(4π)))  R=4.30 cm  H=17.21 cm

youhavetominimizeS=2πR2+πRHundertheconstrainV=πR2H=1ltH=VπR2S=2πR2+VRmin(S)SR=4πRVR2=0R=3V4πR=4.30cmH=17.21cm

Commented by iloveisrael last updated on 18/May/21

r ≈ 5.4 cm

r5.4cm

Answered by iloveisrael last updated on 18/May/21

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