SOLUTION: Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume?
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Question 218034: Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Dalton has a closed rectangular box with a square base at least 10 inches long
have a surface area of 900 square inches.
what dimensions will give the box a maximum volume?
;
Let x = the side of the square base
Actually the maximum is when the box is a perfect cube, therefore
let x = the height of the box also
:
Surface area equation, find h:
6x^2 = 900
simplify divide by 6
x^2 = 150
x =
x = 12.247"
:
Max vol: 12.247 by 12.247 by 12.247, and 12.247^3 = 1836.9 cu/in
:
You can prove this:
let the height = h,
:
Surface area equation, find h:
2x^2 + 4xh = 900
simplify divide by 2
x^2 + 2xh = 450
2xh = -x^2 + 450
h =
:
Volume equation
V = x^2 * h
Replace h
V = x^2()
V = x()
V = x()
Graph this equation y=V
:
Shows max volume when x is a little over 12"; vol is about 1800 cu/in
