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(r

^{2}+ R^{2}+ 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(R

^{2}+ r^{2})In which,

ris the radius of the smaller circle

Ris the radius of the bigger circle

lis the slant height of the frustum of a cone.

**Examples:**

**Example1:**

**Input:**

Given smaller radius = 3 Given bigger radius = 6 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 bigger radius = 7 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. gvn_smallrradiuss = 3 # Give the radius of the bigger circle as static input and store it in another variable. gvn_biggradiuss = 6 # 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 * \ (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss + gvn_smallrradiuss * gvn_biggradiuss) # 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 * \ (gvn_biggradiuss + gvn_smallrradiuss) # 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 * \ (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss) # 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; double gvn_smallrradiuss = 3; int gvn_biggradiuss = 6; int gvn_slantheigt = 8; int gvn_heigt = 10; double rslt_vol = 1 / 3 * pi_val * gvn_heigt * (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss + gvn_smallrradiuss * gvn_biggradiuss); double curvd_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss); double totl_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss) + pi_val * gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss; // 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 * \ (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss + gvn_smallrradiuss * gvn_biggradiuss) # 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 * \ (gvn_biggradiuss + gvn_smallrradiuss) # 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 * \ (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss) # 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