SOLUTION: A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. Find the dimensions of the package o

Algebra ->  Testmodule -> SOLUTION: A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. Find the dimensions of the package o      Log On


   

Question 1125975: A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
Radius = ? in
Length = ? in
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
r radius
x length
combined length and girth, x%2B2pi%2Ar=132
volume x%2Api%2Ar%5E2

v=%28132-2pi%2Ar%29pi%2Ar%5E2
v=132pi%2Ar%5E2-2pi%5E2%2Ar%5E3

dv%2Fdr=264pi%2Ar-6pi%5E2%2Ar%5E2=0

44r-pi%5E2%2Ar%5E2=0

r%2844-pi%5E2%2Ar%29=0

r=0 makes no sense here.

44=pi%5E2%2Ar

highlight_green%28r=44%2Fpi%5E2%29-------radius for maximum volume.

x=132-2pi%2A%2844%2Fpi%5E2%29
.
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