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Python | Percentage increase in hemisphere volume if radius is increased

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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.

Input : 
Output : 
72.8 %
Input : 
Output : 
391.3 % 

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 * x
                + (3 * pow(x, 2)) / 100, '%')
# Driver code
x = 10.0

Output : 

percentage increase in the volume of the hemisphere is  33.1 %

Time Complexity: O(log x) because pow function would take logarithmic time

Auxiliary Space: O(1)


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Last Updated : 20 Feb, 2023
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