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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.
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?
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.
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 $V$.
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.
Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.
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...
