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# Python Program to calculate the volume and area of Sphere

A **sphere (solid)** is usually considered a two-dimensional figure even though the figure is seen in three planes from its center. The main reason for this is that, a sphere is only measured using its radius.

However, a **hollow sphere** is considered a three-dimensional figure since it contains space within its spherical walls and has two different radii to measure its dimensions.

The spherical figure only has **total surface area** since there is only one dimension to measure the entire object. The formula to calculate the surface area of a sphere is −

**Area of solid sphere** − $\mathrm{{4\pi r^2}}$

The volume of a sphere is considered as the mass held by the circular walls of the object. The formula to calculate volume of a sphere is given as −

**Volume of solid sphere** − $\mathrm{{\frac{4}{3}\pi r^3}}$

**Volume of hollow sphere** − $\mathrm{{\frac{4}{3}\pi(R\:-\:r)^3}}$

Where, R is the radius of outer sphere and r is the radius of inner sphere.

### Input Output Scenarios

Let us look at some input output scenarios to calculate the area and volume of a sphere −

Assume the area and volume to be found is of a solid sphere −

Input: 7 // 7 is the radius Result: Area - 314.1592653589793 Volume - 359.188760060433

Assume the area and volume to be found is of a hollow sphere −

Input: (7, 5) // 7 is the outer radius, 5 is the inner radius Result: Area - 314.1592653589793 // Area is same Volume - 100.53096491487338

## Using Mathematical Formula

In the python program, we use the discussed mathematical formulae and calculate the area and volume of the sphere. We import the match library to use the *pi* constant.

### Example

Following is an example to find the area and volume of the spherical 3D figure −

import math R = 7 #outer radius of sphere r = 5 # inner radius of sphere #calculating area of solid sphere area = 4*(math.pi)*(r)*(r) #calculating volume of hollow sphere volume_hollow = 4*(math.pi)*(R - r)*(R - r)*(R - r) #calculating volume of solid sphere volume_solid = (1/3)*(math.pi)*(R)*(R)*(R) #displaying output print("Area of the sphere: ", str(area)) print("Volume of the hollow sphere: ", str(volume_hollow)) print("Volume of the solid sphere: ", str(volume_solid))

### Output

The output is displayed as given below −

Area of the sphere: 314.1592653589793 Volume of the hollow sphere: 100.53096491487338 Volume of the solid sphere: 359.188760060433

## Function to calculate Area and Volume

Python also makes use of functions to improve modularity of the program. In this case, we use a function that calculates sphere’s area and volume.

### Example

In the following python program, we are calculating the area and volume of both solid and hollow spheres using a user-defined function −

import math def sphere_area_volume(R, r): #calculating area of solid sphere area = 4*(math.pi)*(r)*(r) #calculating volume of hollow sphere volume_hollow = 4*(math.pi)*(R - r)*(R - r)*(R - r) #calculating volume of solid sphere volume_solid = (1/3)*(math.pi)*(R)*(R)*(R) #displaying output print("Area of the sphere: ", str(area)) print("Volume of the hollow sphere: ", str(volume_hollow)) print("Volume of the solid sphere: ", str(volume_solid)) R = 7 #outer radius of sphere r = 5 # inner radius of sphere sphere_area_volume(R, r)

### Output

On executing the above code, output is obtained as −

Area of the sphere: 314.1592653589793 Volume of the hollow sphere: 100.53096491487338 Volume of the solid sphere: 359.188760060433

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