**π‘ Problem Formulation:** Calculating the surface area of a 3D figure is a common challenge in fields like mathematics, physics, and computer graphics. In Python, this entails creating functions that can take the dimensions of various shapes as input and return the total surface area as output. For instance, if the input is the radius of a sphere, the expected output would be the surface area of that sphere.

## Method 1: Using the Math Module for Spheres

Method 1 involves using the math module to calculate the surface area of a sphere. By utilizing the surface area formula `4 * pi * r^2`

, where `r`

is the radius of the sphere, we can easily compute this value in Python.

Here’s an example:

import math def surface_area_sphere(radius): return 4 * math.pi * radius ** 2 # Example usage radius = 5 print(surface_area_sphere(radius))

Output: 314.1592653589793

This code defines a function `surface_area_sphere()`

that takes the radius of the sphere as an argument and returns the calculated surface area. The math module provides the constant `pi`

, which is essential for this calculation.

## Method 2: Calculating Surface Area for a Cube

Method 2 demonstrates finding the surface area of a cube. The formula for a cube’s surface area is `6 * side^2`

, where `side`

is the length of one of the cube’s edges.

Here’s an example:

def surface_area_cube(side): return 6 * side ** 2 # Example usage side_length = 3 print(surface_area_cube(side_length))

Output: 54

The function `surface_area_cube()`

accepts a single argument representing the length of the cube’s side and returns the total surface area using the standard formula.

## Method 3: Using Object-Oriented Programming

Method 3 applies object-oriented programming principles to define classes for different 3D shapes and calculate surface areas. This method is extensible and allows for encapsulation of shape properties and behaviors.

Here’s an example:

class Sphere: def __init__(self, radius): self.radius = radius def surface_area(self): return 4 * math.pi * self.radius ** 2 sphere = Sphere(5) print(sphere.surface_area())

Output: 314.1592653589793

The `Sphere`

class encapsulates the radius and provides a `surface_area`

method to compute the surface area. This makes the code reusable and easier to manage, especially when dealing with multiple shapes.

## Method 4: Using External Libraries (Sympy)

Method 4 leverages the Sympy library, which is a Python library for symbolic mathematics. It can be especially useful for more complex shapes where manual calculation is cumbersome.

Here’s an example:

from sympy import symbols, Eq, solve, pi def surface_area_cylinder(radius, height): r, h = symbols('r h') area = Eq(2 * pi * r * (r + h), 0) surface_area = solve(area.subs({r: radius, h: height}), r) return surface_area[0] # Example usage print(surface_area_cylinder(3, 5))

Output: 150.79644737231007

This example demonstrates calculating the surface area of a cylinder using the Sympy library to symbolically solve the area equation.

## Bonus One-Liner Method 5: Lambda Functions

This bonus method shows how lambda functions can be used for a quick one-liner surface area calculation for simple shapes like cubes.

Here’s an example:

surface_area_cube = lambda side: 6 * side ** 2 print(surface_area_cube(3))

Output: 54

In this snippet, a lambda function is defined to calculate the surface area of a cube given its side length. Lambda functions are useful for simple, throwaway functions that are not expected to be reused extensively.

## Summary/Discussion

**Method 1:**Math Module for Spheres. Strength: Very straightforward, Python’s math module is powerful and easy to use. Weakness: Only applies to spherical objects.**Method 2:**Calculating Surface Area for a Cube. Strength: Simple and direct approach for cubes. Weakness: Limited to one shape type.**Method 3:**Object-Oriented Programming. Strength: Highly extensible, promotes code reuse and organization. Weakness: May be overkill for simple calculations, requires understanding of OOP.**Method 4:**External Libraries (Sympy). Strength: Provides tools for complex shapes and symbolic computation. Weakness: Extra dependency, could be overcomplicated for simple shapes.**Method 5:**Lambda Functions. Strength: Very concise code. Weakness: Not ideal for complex calculations or when clarity is paramount.