A beverage company wants their new product to come in 222 ml cans, and the designer wants
Question:
A beverage company wants their new product to come in 222 ml cans, and the designer wants the can to use the least amount of material possible.Find the height and radius of the cylinder with a volume of 222 cm^3 that has the minimum possible surface area. (Note that the cylinder will be closed at both ends.)You may round all calculations to 2 decimal places.Show all steps:
[i.] Find a formula for that expresses one of the height or radius as a function of the other
[ii.] Find a formula for the surface area of the cylinder as a function of a single variable
[iii.] Use the method of optimization to find the required dimensions[iv.] Use either the first derivative test, or the second derivative test to show that the optimized dimensions are a minimum (rather than a maximum)
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna