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Python Program to calculate the volume and area of Cone
A cone is a three-dimensional figure that is formed by connecting infinite line segments from a common point to all the points in a circular base. This common point is also known as an apex. The cone is measured using three dimensions: radius of its circular base, height and lateral height.
The difference between a cone’s height and lateral height is such that− height is measured from the apex to the center of the circular base, while lateral height is a length of line segments connecting apex and any point on the circular base.
The lateral surface area, also known as curved surface area, of a cone is measured using the lateral height and the total surface area is also measured using the lateral height plus the area of circular base. The formulae to calculate these areas is as follows
Lateral Surface Area − πrl Total Surface Area − πr(r+l)
The volume of a cone is defined as the space contained by the curved surface and circular base of the cone.
Volume − $\mathrm{{\frac{1}{3}\pi r^2h}}$
Input Output Scenarios
Let us look at some input output scenarios −
Assume the inputs taken as the radius of the circular base, actual height and lateral height, the output is obtained as −
Input: (3, 4, 5) // 3 is radius, 4 is actual height and 5 is lateral height Result: Lateral Surface Area: 47.12388980384689 Total Surface Area: 75.39822368615503 Volume: 37.69911184307752
Using Mathematical Formulae
We use standard mathematical formulae to find the surface areas and volume of a cone. The input requirements are radius, lateral height and actual height of the cone. Let us look a simple python example to understand it better.
Example
Following example implements the calculation of surface areas and volume of a cone with a certain radius and heights.
import math l = 5 h = 4 r = 3 #calculating the lateral surface area lsa = (math.pi)*r*l print("Lateral Surface Area: ", str(lsa)) #calculating the total surface area tsa = (math.pi)*r*(r+l) print("Total Surface Area: ", str(tsa)) #calculating the volume vol = (1/3)*(math.pi)*r*r*h print("Volume: ", str(vol))
Output
On compiling and executing the program above, the output is obtained as −
Lateral Surface Area: 47.12388980384689 Total Surface Area: 75.39822368615503 Volume: 37.69911184307752
Function to Calculate Area and Volume
Python also allows user-defined functions which can be declared using the def keyword with as many arguments required. In this example, we will create functions to calculate the surface areas and volume of the cone.
Example
In the following example, the input taken by the program will be radius, height and lateral height. User-defined functions are declared to calculate the surface areas and volume.
import math def cone_lsa(r, l): #calculating the lateral surface area lsa = (math.pi)*r*l print("Lateral Surface Area: ", str(lsa)) def cone_tsa(r, l): #calculating the total surface area tsa = (math.pi)*r*(r+l) print("Total Surface Area: ", str(tsa)) def cone_vol(r, h): #calculating the volume vol = (1/3)*(math.pi)*r*r*h print("Volume: ", str(vol)) l = 5 h = 4 r = 3 cone_lsa(r, l) cone_tsa(r, l) cone_vol(r, h)
Output
The output for the code above is displayed as follows −
Lateral Surface Area: 47.12388980384689 Total Surface Area: 75.39822368615503 Volume: 37.69911184307752
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