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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 11.10.2 .
A cylindrical soda can holds about 355 cc of liquid. In this activity, we want to find the dimensions of such a can that will minimize the surface area. For the sake of simplicity, assume the can is a perfect cylinder.
What are the variables in this problem? Based on the context, what restriction(s), if any, are there on these variables?
What quantity do we want to optimize in this problem? What equation describes the constraint? (You need to decide which of these functions plays the role of
\(f\) and which plays the role of
\(g\) in our discussion of Lagrange multipliers.)
Find
\(\lambda\) and the values of your variables that satisfy Equation
(11.10.1) in the context of this problem.
Determine the dimensions of the pop can that give the desired solution to this constrained optimization problem.
