Math Problem Statement
An open-top cylindrical container is to have a volume
729
cmcubed
.
What dimensions (radius and height) will minimize the surface area?
Question content area bottom
Part 1
The radius of the can is about
enter your response here
cm and its height is about
enter your response here
cm.
(Do not round until the final answer. Then round to two decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Calculus
Geometry of Solids
Formulas
Volume of a cylinder: V = πr²h
Surface area of an open-top cylinder: A = πr² + 2πrh
Theorems
Optimization using derivatives
Critical points of a function
Suitable Grade Level
Grades 11-12
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