SOLUTION: A parcel delivery service accepts cylindrical packages whose length L, plus girth, does not exceed 120 inches. A shipper who uses cylindrical cartons, perforated, wishes to design

Question 1195968: A parcel delivery service accepts cylindrical packages whose length L, plus girth, does not exceed 120 inches. A shipper who uses cylindrical cartons, perforated, wishes to design to a carton with maximum ventilation (area). What should be the length and radius of the carton?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A parcel delivery service accepts cylindrical packages whose length L, plus girth, does not exceed 120 inches.
The girth will be the circumference of the cylinder, therefore

A shipper who uses cylindrical cartons, perforated, wishes to design to a carton with maximum ventilation (area).
What should be the length and radius of the carton?
We can ignore the area of the ends

replace L

arrange like a quadratic equation
= 0
using the axis of symmetry (max area occurs) x = b/(2a), where

Cancel -8 and pi

r = 9.55 inches is the radius for max surface area
:
find the length

L = 60 inches is the length

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