# python tutorial - Python Program to find Volume and Surface Area of a Cone - learn python - python programming

- 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

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

## 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:

- If we know the radius and height of a Cone then we calculate the Surface Area of Cone using the below formula:

- Because radius, height and Slant make the shape as right-angled Triangle. So, Using the Pythagoras theorem:

## 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:

## 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

## 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.

- 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

- Next, We are calculating Volume, Surface Area, Lateral Surface Area and Length of a Side (Slant) of a Cone using their respective Formulas:

- Following print statements will help us to print the Volume and Surface area of a Cube

## Output

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

- 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

## 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

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