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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.
- Optimization of an open box
If 900 square cm of material is available to make a box with...
- Largest volume of an open box.
If 1200 $cm^2$ of material is available to make a box with a...
- Optimization of an open box
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.
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.
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...
21 Δεκ 2020 · The remaining flaps are folded to form an open-top box. Step 1: We are trying to maximize the volume of a box. Therefore, the problem is to maximize \(V\). Step 2: The volume of a box is \(V=L⋅W⋅H\), where \(L,W,\)and \(H\) are the length, width, and height, respectively.
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: $$ x^2 + 4xh = 1200 = P$$
