Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Geometry
Differentiation
Volume Maximization
Formulas
Surface Area (S) of open-top cylinder: S = πr² + 2πrh
Volume (V) of a cylinder: V = πr²h
Optimization through differentiation: dV/dr = 0
Theorems
Maximization using the first derivative test
Suitable Grade Level
Grades 10-12 (Pre-Calculus/Calculus level)
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