Math Problem Statement
A cylindrical can has a volume of 686 pi cm cubed. What dimensions yield the minimum surface area? Question content area bottom Part 1 The radius of the can with the minimum surface area is enter your response here cm. (Simplify your answer.) Part 2 The height of the can with the minimum surface area is enter your response here cm. (Simplify your answer.)
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Optimization
Derivatives
Cylindrical Volume and Surface Area
Formulas
Volume of a cylinder: V = πr²h
Surface area of a cylinder: S = 2πr² + 2πrh
Derivative of surface area with respect to radius: dS/dr = 4πr - 1372π/r²
Theorems
Critical points found using derivatives
Optimization of functions using calculus
Suitable Grade Level
Grades 10-12
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