﻿ volume of a open cardboard box

#### Solve the problem.Suppose that an open box is to be …

Solve the problem.Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 384 cubic inches, find the original dimensions of the sheet of cardboard.

#### What is the maximum volume of an open topped box made from ...

Open topped boxes 1 ©MGW2017 What is the maximum volume of an open topped box made from a 20cm x 20cm sheet of cardboard? When squares measuring scm x scm are cut from the corners the box will have a base measuring (20 – 2s) cm by (20 – 2s) cm and a height of s cm. S cm (20-2s) cm s cm This box has volume 𝑉=𝑠(20−2𝑠)2

#### A cardboard box of 108in cubed volume with a square …

31-10-2010· A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides. Find the value of h that maximizes the volume of the box if A = 7. You can view more similar questions or ask a new question.

#### Volume of Open Box Made From Rectangle with Squares …

15-10-2016· Learn how to find the volume of an open box made from a rectangle with squares cut out of the corners. We discuss the domain restrictions, the graph, and ho...

#### Surface Area and Volume of Box Calculator

a = hw b = hl c = wl SA = 2[a + b + c] V = hwl Where, h = Height of Box l = Length of Box w = Width of Box SA = Total Surface Area of Box V = Volume of Box Example: Calculate the total surface area and volume of a box with the height of 10 cm, width of 15 cm, and length of 8 cm.

#### A cardboard box of 108in cubed volume with a square base ...

31-10-2010· A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must . math. A rectangular box with a volume of 320 cubic units is to be constructed with a square base and top.

#### Determine the Maximum Volume of an Open Top Box …

09-10-2016· This video explains how to analyze the graph of a volume function of an open top box to determine the maximum volume. The box is formed but cutting corners ...

#### Polynomial Models: Open Box - MATHguide

You have a cardboard sheet that is 51 inches long by 43 inches wide. Problem: Congruent squares (x by x square inches in size, red in color in the diagram above) are cut from the corners of the cardboard. Once cut, the cardboard is folded upward to form an open box. What is the length of the squares that must be cut in order to maximize the volume ...

#### (Get Answer) - 94. Volume of a Box An open box is to be ...

22-11-2019· 94. Volume of a Box An open box is to be made from a square piece of cardboard with the dimensions 30 inches by 30 inches by cutting out squares of area x 2 from each corner, as shown in the figure. a. Express the volume V of the box as a function of x.. b. State the domain of V.

#### calculus - Optimize volume of an open cardboard box …

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. For this I started by drawing some pictures and writing some things down as shown:

#### Rectangular Box with Maximum Volume | Flapped Lid

This means you should cut 2 by 2 squares from the corners and sides of the cardboard to build a box with maximal volume. The box will be 2 inches high, 6 inches wide, and 9 inches long, yielding a volume of 108 cubic inches.

#### calculus - Maximum volume of a box with a lid that can be ...

18-03-2015· Snacks will be provided in a box with a lid (made by removing squares from each corner of a rectangular piece of card and then folding up the sides) You have a piece of cardboard …

#### Polynomial Models: Open Box - MATHguide

Polynomial Models: Open Box. Status: Waiting for your answers. Given: You have a cardboard sheet that is 51 inches long by 43 inches wide. Problem: Congruent squares (x by x square inches in size, red in color in the diagram above) are cut from the corners of the cardboard. Once cut, the cardboard is folded upward to form an open box.

#### Function Expressing Volume of a Cardboard Box

04-02-2021· A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in. by 17 in. by cutting equal squares from the four corners and turning up the sides. (a) Find a mathematical model expressing the volume of the box as a function of the length of the side of the square cut out.

#### Volume of a Box Calculator - Box Volume Calculator

Volume of a box formula. The volume of a rectangular box can be calculated if you know its three dimensions: width, length and height. The formula is then volumebox = width x length x height. Illustration below: Measuring the sides of a rectangular box or tank is easy.

#### Solved: Volume of a Box An open box with a volume of …

Volume of a Box An open box with a volume of 1500 cm3 is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Show that this can be done in two different ways, and find the exact dimensions of the box …

#### SOLVED:Volume of a Box An open box is to be const…

This is 40 minus two X in this width is 20 minus two X. Um, and find the volume. If you imagine folding this box together, our height is gonna be extends. Its volume appears just gonna be a high time. That with time, the value I wit, um imagine folding it opens.