SOLUTION: Take a 9in x 12in piece of construction paper and make an open box with no lid that will maxamize volume. You may cut and tape the construction paper as many times as needed. The b

Question 91215This question is from textbook
: Take a 9in x 12in piece of construction paper and make an open box with no lid that will maxamize volume. You may cut and tape the construction paper as many times as needed. The box will compare among the classes boxes and I want the box that holds the most rice krispies. Include an information sheet that explains why you chose the dimentions. This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Take a 9 in x 12 in piece of construction paper and make an open box with no lid that will maximize volume. You may cut and tape the construction paper as many times as needed. The box will compare among the classes boxes and I want the box that holds the most rice Krispies. Include an information sheet that explains why you chose the dimensions.
:
Let x = length of the side of the squares cut out of the corners to make the box
x also = the height of the box
:
Length of box = (12-2x)
Width of box = (9-2x)
Height of box = x
:
Volume = y
:
y = x* (12-2x)*(9-2x)
y = x(108 - 42x + 4x^2)
y = 4x^3 - 42x^2 + 108x
:
The best way to find the max volume is to graph it:

:
Using a Ti83 with this same equation, x = 1.7 is the max volume
:
That makes the dimensions:
Length: 12 - 2(1.7) = 8.6 in
Width: 9 - 2(1.7) = 5.6 in
Height: = 1.7 in
:
Max Vol = 8.6 * 5.6 * 1.7 = 81.87 cu inches
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