SOLUTION: Mr.Green has 8.5 by 11 inch cardboard sheets. As a class project Mr.Green asked his students make an open top box under these conditions:
1.) each box must be made by cutting smal
Question 193600: Mr.Green has 8.5 by 11 inch cardboard sheets. As a class project Mr.Green asked his students make an open top box under these conditions:
1.) each box must be made by cutting small squares from each corner of a cardboard sheet
2.) The box must have a volume of 48in^3
3.) The amount of cardboard waste must be minimized
What is the approximate side length for the small squares that would be cut from the cardboard sheet? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Mr.Green has 8.5 by 11 inch cardboard sheets. As a class project Mr.Green asked
his students make an open top box under these conditions:
:
1.) each box must be made by cutting small squares from each corner of a cardboard sheet
2.) The box must have a volume of 48in^3
3.) The amount of cardboard waste must be minimized
What is the approximate side length for the small squares that would be cut from the cardboard sheet?
:
Let x = side length of the cut-out squares
:
then box dimensions will be
(8.5-2x) by (11-2x) by x
:
Vol
(8.5-2x)*(11-2x)*x = 48 cu/in
:
you can check this using x = .7
(11-1.4)*(8.5-1.4)*.7 = 47.7 ~ 48
:
Note that the 3rd intercept ~ 6.4 is obviously on valid
FOIL to find the area of the bottom
93.5 -17x - 22x + 4x^2
Multiply by the height (x) to create an equation for the vol of 48 cu/in
x(4x^2 - 39x + 93.5) = 48
4x^3 - 39x^2 + 93.5x - 48 = 0
;
Plot his equation on a graph
Choose the lowest value x intercept for mimimum waste
x = .70646 (found on a graphing calc)
:
You can check this on a calc
(8.5-1.4)*(11-1.4)*.7 ~ 48
