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 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