 # Python Program for Volume and Surface Area of Frustum of Cone

Given the height, slant height, smaller and bigger radius of a frustum cone, the task is to find the volume and surface area of the frustum of a given cone in python.

Frustum of a Cone :

A frustum in geometry is the portion of a solid (typically a cone or pyramid) that lies between one or two parallel planes that cut it.
The portion of a solid between a plane parallel to the base and a right circular cone is known as the frustum of a cone.

A right circular cone is shown below:

After being cut by a plane parallel to its base, the right circular cone produces the following frustum:

which has a circular base with radius R at the bottom, a circular upper portion with radius R height h, and a slant height l.

Formulas:

volume of the frustum of a cone = 1/3 * pi * h(r2 + R2 + r*R)

The curved surface area of a frustum of a cone = pi * l(R+r)

The total surface area of a frustum of a cone = pi * l(R+r) + pi(R2 + r2)

In which,

r is the radius of the smaller circle

R is the radius of the bigger circle

l is the slant height of the frustum of a cone.

Examples:

Example1:

Input:

Given smaller radius = 3
Given slant height = 8
Given height  = 10

Output:

The Volume of above given Frustum of Cone =  659.7344572538565
The curved surface area of the above given frustum of Cone =  226.1946710584651
The total surface area of the above given frustum of Cone :  367.5663404700058

Example2:

Input:

Given smaller radius = 4
Given slant height = 10
Given height = 15

Output:

The Volume of above given Frustum of Cone = 1460.8405839192537
The curved surface area of the above given frustum of Cone = 345.57519189487726
The total surface area of the above given frustum of Cone : 549.7787143782139

## Program for Volume and Surface Area of Frustum of Cone in Python

Below are the ways to find the volume and surface area of the frustum of a given cone in python:

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

Approach:

• Import math module using the import keyword.
• Get the value of pi using the math.pi function and store it in a variable.
• Give the radius of the smaller circle as static input and store it in a variable.
• Give the radius of the bigger circle as static input and store it in another variable.
• Give the slant height of the frustum cone as static input and store it in another variable.
• Give the height as static input and store it in another variable.
• Calculate the volume of the frustum of a cone using the above given mathematical formula and store it in another variable.
• Calculate the curved surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.
• Calculate the total surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.
• Print the volume of the frustum of a cone.
• Print the curved surface area of a frustum of a cone.
• Print the Total surface area of a frustum of a cone.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Get the value of pi using the math.pi function and store it in a variable.
pi_val = math.pi
# Give the radius of the smaller circle as static input and store it in a variable.
# Give the radius of the bigger circle as static input and store it in another variable.
# Give the slant height of the frustum cone as static input and store it in
# another variable.
gvn_slantheigt = 8
# Give the height as static input and store it in another variable.
gvn_heigt = 10
# Calculate the volume of the frustum of a cone using the above given mathematical
# formula and store it in another variable.
rslt_vol = 1 / 3 * pi_val * gvn_heigt * \
# Calculate the curved surface area of a frustum of a cone using the above given
# mathematical formula and store it in another variable.
curvd_surfce_area = pi_val * gvn_slantheigt * \
# Calculate the total surface area of a frustum of a cone using the above given
# mathematical formula and store it in another variable.
totl_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss) + pi_val * \
# Print the volume of the frustum of a cone.
print("The Volume of above given Frustum of Cone = ", rslt_vol)
# Print the curved surface area of a frustum of a cone.
print("The curved surface area of the above given frustum of Cone = ", curvd_surfce_area)
# Print the Total surface area of a frustum of a cone.
print("The total surface area of the above given frustum of Cone : ", totl_surfce_area)

#include <cmath>
#include <iostream>

using namespace std;

int main()
{
int argc = 2;
double pi_val = M_PI;
int gvn_slantheigt = 8;
int gvn_heigt = 10;
double rslt_vol
= 1 / 3 * pi_val * gvn_heigt
double curvd_surfce_area
= pi_val * gvn_slantheigt
double totl_surfce_area
= pi_val * gvn_slantheigt
// Print the volume of the frustum of a cone.
cout << "The Volume of above given Frustum of Cone = "
<< rslt_vol << endl;
// Print the curved surface area of a frustum of a cone.
cout << "The curved surface area of the above given "
"frustum of Cone = "
<< curvd_surfce_area << endl;
// Print the Total surface area of a frustum of a cone.
cout << "The total surface area of the above given "
"frustum of Cone :"
<< totl_surfce_area;
}

Output:

The Volume of above given Frustum of Cone =  659.7344572538565
The curved surface area of the above given frustum of Cone =  226.1946710584651
The total surface area of the above given frustum of Cone :  367.5663404700058

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

Approach:

• Import math module using the import keyword.
• Get the value of pi using the math.pi function and store it in a variable.
• Give the radius of the smaller circle as user input using the float(input()) function and store it in a variable.
• Give the radius of the bigger circle as user input using the float(input()) function and store it in another variable.
• Give the slant height of the frustum cone as user input using the float(input()) function and store it in another variable.
• Give the height as user input using the float(input()) function and store it in another variable.
• Calculate the volume of the frustum of a cone using the above given mathematical formula and store it in another variable.
• Calculate the curved surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.
• Calculate the total surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.
• Print the volume of the frustum of a cone.
• Print the curved surface area of a frustum of a cone.
• Print the Total surface area of a frustum of a cone.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Get the value of pi using the math.pi function and store it in a variable.
pi_val = math.pi
# Give the radius of the smaller circle as user input using the float(input()) function
# and store it in a variable.
gvn_smallrradiuss = float(input("Enter some random number = "))
# Give the radius of the bigger circle as user input using the float(input()) function
# and store it in another variable.
gvn_biggradiuss = float(input("Enter some random number = "))
# Give the slant height of the frustum cone as user input using the float(input()) function
# and store it in another variable.
gvn_slantheigt = float(input("Enter some random number = "))
# Give the height as user input using the float(input()) function and
# store it in another variable.
gvn_heigt = float(input("Enter some random number = "))
# Calculate the volume of the frustum of a cone using the above given mathematical
# formula and store it in another variable.
rslt_vol = 1 / 3 * pi_val * gvn_heigt * \
# Calculate the curved surface area of a frustum of a cone using the above given
# mathematical formula and store it in another variable.
curvd_surfce_area = pi_val * gvn_slantheigt * \
# Calculate the total surface area of a frustum of a cone using the above given
# mathematical formula and store it in another variable.
totl_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss) + pi_val * \
# Print the volume of the frustum of a cone.
print("The Volume of above given Frustum of Cone = ", rslt_vol)
# Print the curved surface area of a frustum of a cone.
print("The curved surface area of the above given frustum of Cone = ", curvd_surfce_area)
# Print the Total surface area of a frustum of a cone.
print("The total surface area of the above given frustum of Cone : ", totl_surfce_area)


Output:

Enter some random number = 4
Enter some random number = 7
Enter some random number = 10
Enter some random number = 15
The Volume of above given Frustum of Cone = 1460.8405839192537
The curved surface area of the above given frustum of Cone = 345.57519189487726
The total surface area of the above given frustum of Cone : 549.7787143782139