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26 Μαΐ 2020 · Maximizing the volume of an open-top box. Example. A ???5\times7??? piece of paper has squares of side-length ???x??? cut from each of its corners, such that folding up the sides will create a box with no top. Find the value of ???x??? that maximizes the volume of the open-top box. First, we’ll sketch an image of the flat piece of paper.
21 Δεκ 2020 · A rectangular box with a square base, an open top, and a volume of \(216 in.^3\) is to be constructed. What should the dimensions of the box be to minimize the surface area of the box? What is the minimum surface area?
If $1200\ \mathrm{cm}^2$ of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 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 $V$.
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...
In this activity, students will work on a famous math problem exploring the volume of an open box. The aim is to create an open box (without a lid) with the maximum volume by cutting identical squares from each corner of a rectangular card.
In the following example, we look at constructing a box of least surface area with a prescribed volume. It is not difficult to show that for a closed-top box, by symmetry, among all boxes with a specified volume, a cube will have the smallest surface area.
15 Απρ 2015 · The Volume of a box with a square base x by x cm and height h cm is V = x2h. The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.
