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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.
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?
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...
21 Μαρ 2023 · $$Volume= xy \left(\frac{A-xy}{2(x+y)}\right)$$ Then I need to find $\frac{d}{dx} xy \left(\frac{A-xy}{2(x+y)}\right)$ and $\frac{d}{dy} xy \left(\frac{A-xy}{2(x+y)}\right)$ Here are the derivatives $$\frac{d}{dx} xy \left(\frac{A-xy}{2(x+y)}\right)=\frac{y^2(a-x^2-2xy)}{2(x^2+y^2+2xy)}$$ $$\frac{d}{dy} xy \left(\frac{A-xy}{2(x+y)}\right ...
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. ...
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.
