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

In the previous article, we have discussed Python Program for Volume of Pyramid
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:

### 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