# A 24-centimeter by 119-centimeter 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? Enter the area of the square and do not include any units in your answer.

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A 24-centimeter by 119-centimeter 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? Enter the area of the square and do not include any units in your answer.

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Step 1

The 24-cm by 119-cm piece of cardboard used to make an open top box by removing from each corner of the cardboard.

Consider the size of the square cut be x. Take the length of the box be 119–2x, width of the box be 24–2x and the height of the box be x.

Step 2

Obtain the volume of the box as follows.

Step 3

Obtain the derivative of the above obtained volume and se...

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