SOLUTION: You are to construct an open box
from a rectangular sheet of cardboard that measures 18
inches by 25 inches. To assemble the box, you make the four
cuts shown in the figure bel
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-> SOLUTION: You are to construct an open box
from a rectangular sheet of cardboard that measures 18
inches by 25 inches. To assemble the box, you make the four
cuts shown in the figure bel
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Question 1139325: You are to construct an open box
from a rectangular sheet of cardboard that measures 18
inches by 25 inches. To assemble the box, you make the four
cuts shown in the figure below and then fold on the dashed
lines. What value of x (to the nearest 0.01 inch) will produce a
box with maximum volume? What is the maximum volume (to
the nearest 0.1 cubic inch)?
Figure: https://i.imgur.com/lPeHsph.png Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! You are to construct an open box from a rectangular sheet of cardboard that measures 18 inches by 25 inches.
To assemble the box, you make the four cuts shown in the figure below and then fold on the dashed lines.
What value of x (to the nearest 0.01 inch) will produce a box with maximum volume?
:
From the diagram we can see the dimensions will be (25-4x) by (18-2x) and the height will be x
the volume then
V = (25-4x)*(18-2x)*x
FOIL
V = (450-50x-72x+8x^2)*x
V = 8x^3 - 122x^2 + 450x
We can plot this
Max volume is when x = 2.41"
