ATAR Notes: Forum
Uni Stuff => Science => Faculties => Mathematics => Topic started by: QuantumJG on August 14, 2010, 11:31:39 am
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Lagranges multipliers question!
Design a cylindrical can with a lid to contain 1L of water, using the minimal amount of metal.
Here's how I tackled it.
S(r,h) = 2πrh + πr2
V(r,h) = πr2h - 1 = 0
So
Let gradS = λgradV
So (2πh + 2πr, 2πr) = λ(2πrh,πr2)
So
πr2h - 1 = 0 ...1
h + r = λrh ...2
2 = λr ...3 because r can't be zero!
Anyway I got r = h = (π)-3
But according to the book it's wrong!