SOLUTION: Please help me solve this word problem: The sum of the length and girth (circumference of a circular cross section) of a cylindrical container must be 144 inches. Find the dimens

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Please help me solve this word problem: The sum of the length and girth (circumference of a circular cross section) of a cylindrical container must be 144 inches. Find the dimens      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1075946: Please help me solve this word problem: The sum of the length and girth (circumference of a circular cross section) of a cylindrical container must be 144 inches. Find the dimensions of the container that will maximize its volume.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the length and girth (circumference of a circular cross section) of a cylindrical container must be 144 inches.
Find the dimensions of the container that will maximize its volume.
:
let h = the length of the cylindrical container
let r = the radius
the circumference = 2%2Api%2Ar
then
h = 144 -(2*pi*r)
The vol of a cylinder: V+=+pi%2Ar%5E2%2Ah
V+=+pi%2Ar%5E2%2A%28144-%282%2Api%2Ar%29%29
Graphing, x=radius, y=volume

A radius of 15.3 will give a max volume of 35200 cu/in the green line
Find the height
144 - (2*pi*15.3) = 47.86 in is the height
:
;
Check this
v+=+pi%2A15.3%5E2+%2A+47.86
V = 35,202 cu/inches