Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Surface Area
Derivatives
Geometry
Formulas
Volume of cylinder: V = πr^2h
Surface area of open-top cylinder: A = πr^2 + 2πrh
Derivative to minimize surface area: dA/dr = 2πr - 324/r^2
Theorems
Optimization using derivatives
Surface area and volume relationships
Suitable Grade Level
Grades 10-12
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