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Python | Percentage increase in hemisphere volume if radius is increased
  • Difficulty Level : Expert
  • Last Updated : 27 Dec, 2019

Given that the radius of a hemisphere is increased by a fixed percentage so, the target is to calculate the percentage increase in the volume of the hemisphere.

Examples:
Input :
20
Output :
72.8 %

Input :
70
Output :
391.3 %

Approach:
Let, the radius of the hemisphere = a
Given percentage increase = x%
Volume before increase = \frac{2}{3} * 3.14*a^3
New radius after increase = a + \frac{ax}{100}
So, new volume = \frac{2}{3}*3.14*(a^3 + (\frac{ax}{100})^3 + \frac{3a^3x}{100} + \frac{3a^3x^2}{10000})
Change in volume = \frac{2}{3}*3.14*((\frac{ax}{100})^3 + \frac{3a^3x}{100} + \frac{3a^3x^2}{10000})
Percentage increase in volume = (\frac{2}{3}*3.14*((\frac{ax}{100})^3 + \frac{3a^3x}{100} + \frac{3a^3x^2}{10000})/\frac{2}{3}*3.14*a^3) * 100 = \frac{x^3}{10000} + 3x + \frac{3x^2}{100}

Below is the Python code implementation of the above mentioned approach.






# Python3 program to find percentage increase 
# in the volume of the hemisphere 
# if the radius is increased by a given percentage 
    
def newvol(x): 
    
    print("percentage increase in the  volume of the"
          " hemisphere is ", pow(x, 3) / 10000 + 3 *
                + (3 * pow(x, 2)) / 100, "%"
    
# Driver code 
x = 10.0
newvol(x) 

Output :

percentage increase in the volume of the hemisphere is  33.1 %

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