# 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 SidesÂ 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)Â  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)Â  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)Â 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