# Python Program to find Volume and Surface Area of a Cone

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

### Python 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
l = Slant (Length of an edge from top of the cone to edge of a cone)

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)

Because radius, height and Slant make the shape as right-angled Triangle. So, Using the Pythagoras theorem:
l² = h² + r²
l = √h² + r²

### Python 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

## Python Program to find Volume and Surface Area of a Cone

This python 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.

```# Python Program to find Volume and Surface Area of a Cone

import math

height = float(input('Please Enter the Height of a Cone: '))

# Calculate Length of a Slide (Slant)

# Calculate the Surface Area

# Calculate the Volume

# 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)```

Within this Python Program to find Volume and Surface Area of a Cone, 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`

Below Python 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: '))```

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)
# Calculate the Surface Area
# Calculate the Volume
# Calculate the Lateral Surface Area
LSA = math.pi * radius  * l```

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)```

For this Python Program to find Volume and Surface Area of a Cone, 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
=> √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)
It means, Surface Area of a Cone = math.pi * radius * (radius + l)
Surface Area of a Cone = 3.14 * 5 * ( 5 +13) => 3.14 * 5 * 18
Surface Area of a Cone = 282.6

The Volume of a Cone is
Volume of a Cone = 1/3 πr²h
It means, 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
It means, 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)

It means, 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)
=> 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 python 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.

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

import math

# Calculate Length of a Slide (Slant)

# Calculate the Surface Area

# Calculate the Volume

# 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)```

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

``````
Length of a Side (Slant)of a Cone = 11.66
The Surface Area of a Cone = 332.92
The Volume of a Cone = 376.99
The Lateral Surface Area of a Cone = 219.82
>>> Vo_Sa_Cone(5,12)

Length of a Side (Slant)of a Cone = 13.00
The Surface Area of a Cone = 282.74
The Volume of a Cone = 314.16
The Lateral Surface Area of a Cone = 204.20
>>> ``````

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