You are planning to make an open rectangular box from aa 4141-in.-by-8181-in. piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest volume you can make this way, and what is its volume

13058.83 cubic inches

Step-by-step explanation:

Given that a rectangular box is having dimensions as 41x81 inches.

Let x be the side of square cut from all the four corners.

The open box made would have height as x and length 41-2x with width 81-2x

Volume =

Equate first derivative to 0

We get applicable root as x = 8.642

Max volume = 13058.83 cubic inches

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