Python Program for Maximize Volume of Cuboid with Given Sum of Sides

Given the sum of length, breadth, and height of a cuboid say S and the task is to get the maximum volume of a cuboid such that the sum of the side is S.

Examples:

Example1:

Input:

Given sum = 5

Output:

The maximum volume of a cuboid such that the sum of the side { 5 } =  4

Example2:

Input:

Given sum = 11

Output:

The maximum volume of a cuboid such that the sum of the side { 11 } = 48

Program for Maximize Volume of Cuboid with Given Sum of Sides in Python

Below are the ways to get the maximum volume of a cuboid such that the sum of the side is S in python:

Using For Loop (Static Input)
Using For loop (User Input)

Method #1: Using For loop (Static Input)

Approach:

Give the number (sum) as static input and store it in a variable.
Create a function to say Maximum_volume() which takes the given number as an argument and returns the maximum volume of a cuboid such that the sum of the side is the given sum.
Inside the function, take a variable to say maxim_vol and initialize its value to 0.
Take another variable (for length) say a and initialize its value to 1.
Loop till the given sum -1 using the for loop.
Take another variable (for breadth) say b and initialize its value to 1.
Loop till the given sum using another nested for loop.
Subtract the above variables a, b values from the given sum and store it in a variable say c (for height).
Multiply the above a, b, c values and store them in another variable.
Get the maximum value from the above-initialized maxim_vol and above multiplication result using the max() function and store it in another variable.
Return the above result which is the maximum volume of a cuboid.
Pass the given number as an argument to the Maximum_volume() function and print it.
The Exit of the Program.

Below is the implementation:

# Create a function to say Maximum_volume() which takes the given number as an
# argument and returns the maximum volume of a cuboid such that the sum of the side
# is the given sum.



def Maximum_volume(gvn_sum):
  # Inside the function, take a variable and initialize its value to 0.
    maxim_vol = 0

    # Take another variable (for length) say a and initialize its value to 1.
    a = 1
    # Loop till the given sum -1 using the for loop.
    for a in range(gvn_sum - 1):
      # Take another variable (for breadth) say b and initialize its value to 1.
        b = 1

        # Loop till the given sum using the another nested for loop.
        for b in range(gvn_sum):
            # Subtract the above variables a, b values from the given sum and store
            # it in a variable say c.
            c = gvn_sum - a - b
            # Multiply the above a, b, c values and store them in another variable.

            mult = a * b * c
            # Get the maximum value from the above-initialized maxim_vol and above
            # multiplication result using the max() function and store it in
            # another variable.
            maxim_vol = max(maxim_vol, mult)
        # Return the above result which is the maximum volume of a cuboid.
    return maxim_vol


# Give the number (sum) as static input and store it in a variable.
gvn_sum = 5
# Pass the given number as an argument to the Maximum_volume() function
# and print it.
print("The maximum volume of a cuboid such that the sum of the side {", gvn_sum, "} = ", Maximum_volume(
    gvn_sum))

Output:

The maximum volume of a cuboid such that the sum of the side { 5 } =  4

Method #2: Using For loop (User Input)

Approach:

Give the number (sum) as user input using the int(input()) function and store it in a variable.
Create a function to say Maximum_volume() which takes the given number as an argument and returns the maximum volume of a cuboid such that the sum of the side is the given sum.
Inside the function, take a variable to say maxim_vol and initialize its value to 0.
Take another variable (for length) say a and initialize its value to 1.
Loop till the given sum -1 using the for loop.
Take another variable (for breadth) say b and initialize its value to 1.
Loop till the given sum using another nested for loop.
Subtract the above variables a, b values from the given sum and store it in a variable say c (for height).
Multiply the above a, b, c values and store them in another variable.
Get the maximum value from the above-initialized maxim_vol and above multiplication result using the max() function and store it in another variable.
Return the above result which is the maximum volume of a cuboid.
Pass the given number as an argument to the Maximum_volume() function and print it.
The Exit of the Program.

Below is the implementation:

# Create a function to say Maximum_volume() which takes the given number as an
# argument and returns the maximum volume of a cuboid such that the sum of the side
# is the given sum.

def Maximum_volume(gvn_sum):
  # Inside the function, take a variable and initialize its value to 0.
    maxim_vol = 0

    # Take another variable (for length) say a and initialize its value to 1.
    a = 1
    # Loop till the given sum -1 using the for loop.
    for a in range(gvn_sum - 1):
      # Take another variable (for breadth) say b and initialize its value to 1.
        b = 1

        # Loop till the given sum using the another nested for loop.
        for b in range(gvn_sum):
            # Subtract the above variables a, b values from the given sum and store
            # it in a variable say c.(for height)
            c = gvn_sum - a - b
            # Multiply the above a, b, c values and store them in another variable.

            mult = a * b * c
            # Get the maximum value from the above-initialized maxim_vol and above
            # multiplication result using the max() function and store it in
            # another variable.
            maxim_vol = max(maxim_vol, mult)
        # Return the above result which is the maximum volume of a cuboid.
    return maxim_vol


# Give the number (sum) as user input using the int(input()) function and 
# store it in a variable.
gvn_sum = int(input("Enter some random number = "))
# Pass the given number as an argument to the Maximum_volume() function
# and print it.
print("The maximum volume of a cuboid such that the sum of the side {", gvn_sum, "} = ", Maximum_volume(
    gvn_sum))

Output:

Enter some random number = 11
The maximum volume of a cuboid such that the sum of the side { 11 } = 48