SOLUTION: 4. An open box is to be made from a 16 cm by 30 cm piece of
cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the si
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-> SOLUTION: 4. An open box is to be made from a 16 cm by 30 cm piece of
cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the si
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Question 1202067: 4. An open box is to be made from a 16 cm by 30 cm piece of
cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to
obtain a box with the largest volume? Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Volume of box = length * width * height
Let x be the side of the squares cut off from corners
After cutting and folding x becomes the height of the box
Volume of box = (16-2x)(30-2x)*x
(480 -32x-60x+4x^2)*x
Vx=4x^3 -92x^2+480x
To get maximum volume we find the extrema of the function and Vx =0
dV/dx = 12x^2 - 184x + 480 = 0
This will reduce to:
3x^2 - 46x + 120 = 0
(x - 12)(3x - 10) = 0
So, there are two solutions x=12 x= 10/3
12 not possible because 2x =24 and greater than the side 16
So x= 10/3
Length of the square
