A 22-inch by 70-inch piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a box with the maximum volume

5 Inches

Step-by-step explanation:

Let the side length of the square in inches=y.

Height of the Box = y

Since we are removing the square from both sides

Then the volume of the box,  

We maximize the volume of the box by taking its derivative and solving it for its critical point.

When V'=0

Divide all through by 4 and factor

x cannot be greater than 11. therefore, the value of x=25.6 is extraneous. The side length of the square that should be cut to maximize its volume is 5 inches.

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step-by-step explanation:

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step-by-step explanation:

told you