Question

Write a program that prompts the user to enter the area of the flat cardboard. The program then outputs the length and width of the cardboard and the length of the side of the square to be cut from the corner so that the resulting box is of maximum volume. Calculate your answer to three decimal places. Your program must contain a function that takes as input the length and width of the cardboard and returns the side of the square that should be cut to maximize the volume. The function also returns the maximum volume.

Answer 1

Answer:

A program in C++ was written to prompts the user to enter the area of the flat cardboard.

Explanation:

Solution:

The C++ code:

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;

double min(double,double);

void max(double,double,double&,double&);

int main()

{double area,length,width=.001,vol,height,maxLen,mWidth,maxHeight,maxVolume=-1;

cout<<setprecision(3)<<fixed<<showpoint;

cout<<"Enter the area of the flat cardboard: ";

cin>>area;

while(width<=area)

{length=area/width;

max(length,width,vol,height);

if(vol>maxVolume)

{maxLen=length;

mWidth=width;

maxHeight=height;

maxVolume=vol;

}

width+=.001;

}

cout<<"dimensions of card to maximize the cardboard box which has a volume "

<<maxVolume<<endl;

cout<<"Length: "<<maxLen<<"\nWidth: "<<maxLen<<endl;

cout<<"dimensions of the cardboard box\n";

cout<<"Length: "<<maxLen-2*maxHeight<<"\nWidth: "

<<mWidth-2*maxHeight<<"\nHeight: "<<maxHeight<<endl;

return 0;

}

void max(double l,double w,double& max, double& maxside)

{double vol,ht;

maxside=min(l,w);

ht=.001;

max=-1;

while(maxside>ht*2)

{vol=(l-ht*2)*(w-ht*2)*ht;

if(vol>max)

{max=vol;

maxside=ht;

}

ht+=.001;

}

}

double min(double l,double w)

{if(l<w)

return l;

return w;

}

Note:  Kindly find the output code below

/*

Output for the code:

Enter the area of the flat cardboard: 23

dimensions of card to maximize the cardboard box which has a volume 0.023

Length: 4.796

Width: 4.796

dimensions of the cardboard box

Length: 4.794

Width: 4.794

Height: 0.001

*/