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  • To write Python Program to find Volume and Surface Area of a Cone with example.
  • Before we step into the program, Let see the definitions and formulas behind Surface area of a Cone and Volume of a Cone
 Python Program to find Volume and Surface Area of a Cone

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Surface Area of a Cone

  • If we know the radius and Slant of a Cone then we calculate the Surface Area of Cone using the below formula:
Surface Area = Area of the Cone + Area of Circle

Surface Area = πrl + πr²

Where r = radius and

l = Slant (Length of an edge from top of the cone to edge of a cone)
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  • If we know the radius and height of a Cone then we calculate the Surface Area of Cone using the below formula:
Surface Area = πr² +πr √h² + r²

We can also write it as:

Surface Area = πr (r+√h² + r²)
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  • Because radius, height and Slant make the shape as right-angled Triangle. So, Using the Pythagoras theorem:
l² = h² + r²
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l = √h² + r²
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Volume of a Cone

  • The amount of space inside the Cone is called as Volume.
  • If we know the radius and height of the Cone then we can calculate the Volume using the formula:
Volume = 1/3 πr²h (where h= height of a Cone)

The Lateral Surface Area of a Cone = πrl
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Python Program to find Volume and Surface Area of a Cone

  • This program allows user to enter the value of a radius and height of a Cone.
  • Using these values it will calculate the Surface Area, Volume, length of a side (Slant) and Lateral Surface Area of a Cone as per the formulas.

Sample Code

# Python Program to find Volume and Surface Area of a Cone
 
import math
 
radius = float(input('Please Enter the Radius of a Cone: '))
height = float(input('Please Enter the Height of a Cone: '))
 
# Calculate Length of a Slide (Slant)
l = math.sqrt(radius * radius + height * height)
 
# Calculate the Surface Area
SA = math.pi * radius * (radius + l)
 
# Calculate the Volume
Volume = (1.0/3) * math.pi * radius * radius * height
 
# Calculate the Lateral Surface Area
LSA = math.pi * radius  * l
 
print("\n Length of a Side (Slant)of a Cone = %.2f" %l)
print(" The Surface Area of a Cone = %.2f " %SA)
print(" The Volume of a Cone = %.2f" %Volume);
print(" The Lateral Surface Area of a Cone = %.2f " %LSA)
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Analysis

  • First, We imported the math library using the following statement.
  • This will allow us to use the mathematical functions like math.pi and math.sqrt.
  • If you fail to include this line then math.pi will through an error.
import math
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  • Below statements will ask the user to enter radius and height values and it will assign the user input values to respected variables.
  • Such as first value will be assigned to radius and second value to height
radius = float(input('Please Enter the Radius of a Cone: '))
height = float(input('Please Enter the Height of a Cone: '))
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  • Next, We are calculating Volume, Surface Area, Lateral Surface Area and Length of a Side (Slant) of a Cone using their respective Formulas:
# Calculate Length of a Slide (Slant)
l = math.sqrt(radius * radius + height * height)
# Calculate the Surface Area
SA = math.pi * radius * (radius + l)
# Calculate the Volume
Volume = (1.0/3) * math.pi * radius * radius * height
# Calculate the Lateral Surface Area
LSA = math.pi * radius  * l
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  • Following print statements will help us to print the Volume and Surface area of a Cube
print("\n Length of a Side (Slant)of a Cone = %.2f" %l)
print(" The Surface Area of a Cone = %.2f " %SA)
print(" The Volume of a Cone = %.2f" %Volume);
print(" The Lateral Surface Area of a Cone = %.2f " %LSA)
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Output

 Python Program to find Volume and Surface Area of a Cone

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  • We have entered the Radius of a Cone = 5 and Height = 12

As per the Pythagoras theorem, We can calculate the Slant (Length of a side):
l² = h² + r²
l = √h² + r²
l = √12² + 5²
l = √144 + 25
l = √169
l = 13

The Surface Area of a Cone is
Surface Area of a Cone = πr² +πrl
Surface Area of a Cone = πr (r + l)
Surface Area of a Cone = math.pi * radius * (radius + l)
Surface Area of a Cone = 3.14 * 5 * ( 5 +13)
Surface Area of a Cone = 3.14 * 5 * 18
Surface Area of a Cone = 282.6

The Volume of a Cone is
Volume of a Cone = 1/3 πr²h
Volume of a Cone = (1.0/3) * math.pi * radius * radius * height
Volume of a Cone = (1.0/3) * 3.14 * 5 * 5 * 12;
Volume of a Cone = 314

The Lateral Surface Area of a Cone is
Lateral Surface Area = πrl
Lateral Surface Area = math.pi * radius * l
Lateral Surface Area = 3.14 * 5 * 13
Lateral Surface Area = 204.1

Let us calculate the Radius of a Cone using the radius without using the Slant (Standard Formula):
Surface Area of a Cone = πr² +πr √h² + r²
Surface Area of a Cone = πr (r + √h² + r²)
Surface Area = math.pi * radius * ( radius + math.sqrt ( (height * height) + (radius * radius) ) )
Surface Area of a Cone = 3.14 * 5 * ( 5 + √12² + 5²)
Surface Area of a Cone = 3.14 * 5 * ( 5 + √169)
Surface Area of a Cone = 3.14 * 5 * ( 5 + 13)
Surface Area of a Cone = 3.14 * 5 * 18
Surface Area of a Cone = 282.6

Python Program to find Volume and Surface Area of a Cone using functions

  • This program allows user to enter the value of a radius and height of a Cone.
  • We will pass the radius and height values to the function argument and then it will calculate the Surface Area and Volume of a Cone as per the formula.

Sample Code

# Python Program to find Volume and Surface Area of a Cone using functions
 
import math
 
def Vo_Sa_Cone(radius, height):
    # Calculate Length of a Slide (Slant)
    l = math.sqrt(radius * radius + height * height)
 
    # Calculate the Surface Area
    SA = math.pi * radius * (radius + l)
 
    # Calculate the Volume
    Volume = (1.0/3) * math.pi * radius * radius * height
 
    # Calculate the Lateral Surface Area
    LSA = math.pi * radius  * l
 
    print("\n Length of a Side (Slant)of a Cone = %.2f" %l)
    print(" The Surface Area of a Cone = %.2f " %SA)
    print(" The Volume of a Cone = %.2f" %Volume)
    print(" The Lateral Surface Area of a Cone = %.2f " %LSA)
 
Vo_Sa_Cone(6,10)
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Analysis:

  • First, We defined the function with two argument using def keyword.
  • It means, User will enter the radius and height of a Cone.
  • Using those values, above function will calculate the Surface Area and Volume of a Sphere as we explained in first example

Output

 Python Program to find Volume and Surface Area of a Cone using functions

Learn Python - Python tutorial - Python Program to find Volume and Surface Area of a Cone using functions - Python examples - Python programs

NOTE: We can call the function with arguments in .py file directly or else we can call it from the python shell. Please don’t forget the function arguments


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