We are constructing a box from a rectangular piece of cardboard. The piece of cardboard which measures 20 inches wide and 58 inches long. We will remove a square of size “x” inches from each corner and turn up the edges. Once we remove the squares of size “x” inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable “x”. h=h= w=w= l=l= What is the equation that represents the Volume of the box as a function of the cutsize of the box? V(x)=Vx= What is the restricted domain of this problem? (That is, what x values "make sense"?) ≤x≤≤x≤ What is the restricted range of this problem? (That is, what V values "make sense"?) ≤V(x)≤≤Vx≤ (round to 1 decimal place) To maximize the volume of the newly created box, how much should be cut from each corner? x=x= inches (round to 1 decimal place) What is the maximum volume the box can hold? V=V= in3 (round to 1 decimal place) What is the largest cutsize you can cut out of the paper and still create a box with volume 1455in31455in3? x=x= (round to 1 decimal place)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

We are constructing a box from a rectangular piece of cardboard. The piece of cardboard which measures 20 inches wide and 58 inches long. We will remove a square of size “x” inches from each corner and turn up the edges.

Once we remove the squares of size “x” inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable “x”.