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

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) (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 =
then
h = 144 -(2*pi*r)
The vol of a cylinder:

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 = 35,202 cu/inches

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