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26 Μαΐ 2020 · After cutting out the squares from the corners, the width of the open-top box will be 5-2x, and the length will be 7-2x. We’re being asked to maximize the volume of a box, so we’ll use the formula for the volume of a box, and substitute in the length, width, and height of the open-top box.
If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. The quantity we want to optimize is the volume of the box. Let V be the volume of the box. We want to find the maximum value of V.
If 1200 $cm^2$ of material is available to make a box with a square base and an open top, find the largest possible volume of the box. So I setup my problem like this: $$ x^2 + 4xh = 1200 = P$$
9 Απρ 2020 · If 900 square cm of material is available to make a box with a square base and open top, what is the largest possible volume? The answer is $2598$ cm $^3$ , but I don't know how one gets this answer.
Maximizing the Volume of a Box. An open-top box is to be made from a 24 24 in. by 36 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?
Optimization: Maximizing volume. One of the key applications of finding global extrema is in optimizing some quantity, either minimizing or maximizing it. For example, suppose you wanted to make an open-topped box out of a flat piece of cardboard that is 25" long by 20" wide.
This video provides an example of how to use calculus methods to determine the maximum volume of an open top box with a fixed surface area.https://mathispowe...
