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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.
- Maximum volume of an open box with a square base?
A box with a square base and an open top is to be made. You...
- calculus - Find the maximum volume of a box with an open top and when ...
Find the maximum volume of an open top prism with an...
- Maximum volume of an open box with a square base?
A box with a square base and an open top is to be made. You have 1200cm2 1200 cm 2 of material to make it. What is the maximum volume the box could have? Here's what I did: 1200 =x2 + 4xz; 1200 = x 2 + 4 x z; where x x is length of base and z z is height of box. Also, let the volume of box be V V, then. V =x2z =x2(1200 −x2 4x) = 300x − (0. ...
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.
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.
21 Μαρ 2023 · Find the maximum volume of an open top prism with an isosceles base, if the surface area is constant and length is 1. 2 A closed top box is to be made from piece of cardboard with a surface area of 526.
30 Ιουλ 2024 · To find the volume of a box, simply multiply length, width, and height — and you're good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters. For dimensions that are relatively small whole numbers, calculating volume by hand is easy.
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.
