**Calculate the slant height for the given cone: **In the previous article, we have discussed Python Program to Calculate Sum of Series 1³+2³+3³+….+n³

**The surface area of a cone : **

Formula to calculate its surface area:

Surface Area = Area of a Cone + Area of a Circle

i.e. **Surface Area of cone = πrl + πr²**

In which ‘r’ denotes **radius** and

‘l’ denotes **slant** (Length of an edge from the top of the cone to edge of a cone)

If we know the** radius and height** of a cone, we can use the following formula to calculate its surface area:

Surface Area = πr² +πr √h² + r²

It can also be written as:

**Surface Area of a cone = πr (r+√h² + r²)**

Because the radius, height, and slant combine to form a right-angled triangle. So, using Pythagoras’ theorem:

l² = h² + r²

l = √h² + r²

**The volume of a cone :**

Volume refers to the amount of space inside the Cone. If we know the radius and height of the cone, we can use the following formula to calculate the volume:

**The volume of a cone= 1/3 πr²h** (where h = height of a cone)

**A Cone’s Lateral Surface Area = πrl**

Given the radius and height of a cone, the task is to find the surface area, volume, and lateral surface for a given cone.

- Python Program for Volume and Surface Area of Frustum of Cone
- Python Program to Calculate Volume and Surface Area of Hemisphere
- C Program to Calculate Volume and Total Surface Area of Cone

**Examples:**

**Example 1:**

**Input:**

Given radius = 6.5 Given height = 10

**Output:**

The given cone's slant height = 11.927 The given surface Area of a cone with given radius,height[ 6.5 10 ]= 376.283 The given volume of a cone with given radius,height[ 6.5 10 ]= 442.441 The given lateral surface Area of a cone with given radius,height[ 6.5 10 ]= 243.551

**Example 2:**

**Input:**

Given radius = 4 Given height = 8

**Output:**

The given cone's slant height = 8.944 The given surface Area of a cone with given radius,height[ 4 8 ]= 162.663 The given volume of a cone with given radius,height[ 4 8 ]= 134.041 The given lateral surface Area of a cone with given radius,height[ 4 8 ]= 112.397

## Program to Find Volume and Surface Area of a Cone

Below are the ways to find the surface area, volume, and lateral surface for a given cone.

### Method #1: Using Mathematical Formula (Static Input)

**Approach:**

- Import math module using the import keyword.
- Give the radius of a cone as static input and store it in a variable.
- Give the height of a cone as static input and store it in another variable.
- Calculate the Slant height of a given cone using the above given mathematical formula and math.sqrt() function and store it in another variable.
- Calculate the surface area of a given cone using the above given mathematical formula and math.pi function
- Store it in another variable.
- Calculate the volume of a given cone using the above given mathematical formula and math.pi function
- Store it in another variable.
- Calculate the lateral surface area of a given cone using the above given mathematical formula and math.pi function.
- Store it in another variable.
- Print the slant height of a given cone.
- Print the surface area of a given cone.
- Print the volume of a given cone.
- Print the lateral surface area of a given cone.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Give the radius of a cone as static input and store it in a variable. gvn_rad = 6.5 # Give the height of a cone as static input and store it in another variable. gvn_heigt = 10 # Calculate the Slant height of a given cone using the above given mathematical formula # and math.sqrt() function and store it in another variable. slant_l = math.sqrt(gvn_rad * gvn_rad + gvn_heigt * gvn_heigt) # Calculate the surface area of a given cone using the above given mathematical formula and math.pi function # Store it in another variable. surf_area = math.pi * gvn_rad * (gvn_rad + slant_l) # Calculate the volume of a given cone using the above given mathematical formula and # math.pi function # Store it in another variable. Vol = (1.0/3) * math.pi * gvn_rad * gvn_rad * gvn_heigt # Calculate the lateral surface area of a given cone using the above given mathematical # formula and math.pi function. # Store it in another variable. Laterl_surfcarea = math.pi * gvn_rad * slant_l # Print the slant height of a given cone. print("The given cone's slant height = %.3f" % slant_l) # Print the surface area of a given cone. print( "The given surface Area of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f" % surf_area) # Print the volume of a given cone. print( "The given volume of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f" % Vol) # Print the lateral surface area of a given cone. print( "The given lateral surface Area of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f " % Laterl_surfcarea)

**Output:**

The given cone's slant height = 11.927 The given surface Area of a cone with given radius,height[ 6.5 10 ]= 376.283 The given volume of a cone with given radius,height[ 6.5 10 ]= 442.441 The given lateral surface Area of a cone with given radius,height[ 6.5 10 ]= 243.551

### Method #2: Using Mathematical Formula (User Input)

**Approach:**

- Import math module using the import keyword.
- Give the radius of a cone as user input using the float(input()) function and store it in a variable.
- Give the height of a cone as user input using the float(input()) function and store it in another variable.
- Calculate the Slant height of a given cone using the above given mathematical formula and math.sqrt() function and store it in another variable.
- Calculate the surface area of a given cone using the above given mathematical formula and math.pi function
- Store it in another variable.
- Calculate the volume of a given cone using the above given mathematical formula and math.pi function
- Store it in another variable.
- Calculate the lateral surface area of a given cone using the above given mathematical formula and math.pi function.
- Store it in another variable.
- Print the slant height of a given cone.
- Print the surface area of a given cone.
- Print the volume of a given cone.
- Print the lateral surface area of a given cone.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Give the radius of a cone user input using the float(input()) function and store it in a variable. gvn_rad = float(input("Enter some random number = ")) # Give the height of a cone user input using the float(input()) function and store it in another variable. gvn_heigt = float(input("Enter some random number = ")) # Calculate the Slant height of a given cone using the above given mathematical formula # and math.sqrt() function and store it in another variable. slant_l = math.sqrt(gvn_rad * gvn_rad + gvn_heigt * gvn_heigt) # Calculate the surface area of a given cone using the above given mathematical formula and math.pi function # Store it in another variable. surf_area = math.pi * gvn_rad * (gvn_rad + slant_l) # Calculate the volume of a given cone using the above given mathematical formula and # math.pi function # Store it in another variable. Vol = (1.0/3) * math.pi * gvn_rad * gvn_rad * gvn_heigt # Calculate the lateral surface area of a given cone using the above given mathematical # formula and math.pi function. # Store it in another variable. Laterl_surfcarea = math.pi * gvn_rad * slant_l # Print the slant height of a given cone. print("The given cone's slant height = %.3f" % slant_l) # Print the surface area of a given cone. print( "The given surface Area of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f" % surf_area) # Print the volume of a given cone. print( "The given volume of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f" % Vol) # Print the lateral surface area of a given cone. print( "The given lateral surface Area of a cone with given radius,height[", gvn_rad, gvn_heigt, "]= %.3f " % Laterl_surfcarea)

**Output:**

Enter some random number = 4.5 Enter some random number = 2 The given cone's slant height = 4.924 The given surface Area of a cone with given radius,height[ 4.5 2.0 ]= 133.235 The given volume of a cone with given radius,height[ 4.5 2.0 ]= 42.412 The given lateral surface Area of a cone with given radius,height[ 4.5 2.0 ]= 69.617

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