C++ Program to Find the Surface Area and Volume of a Cube

Introduction

A cube is a three-dimensional geometric figure with six equal square faces. It is one of the simplest and most symmetrical three-dimensional shapes. Understanding how to calculate the surface area and volume of a cube is essential in geometry, engineering, and various practical applications like packaging and construction.

In this article, we will explain how to calculate the surface area and volume of a cube using C++. We'll break the task into clear sections, including the mathematical formulas, the C++ program code, the expected output, and a detailed explanation of the logic behind the program.

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Formula

The calculations for the surface area and volume of a cube are based on its side length, denoted as a. The formulas are:

• Surface Area: The surface area of a cube is calculated as: 6 × a², where a is the length of one side of the cube.
• Volume: The volume of a cube is calculated as: a³, where a is the length of one side of the cube.

These formulas stem from the fact that a cube has six square faces, and its volume is the cube of its side length.

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Code

Here is the C++ program to calculate the surface area and volume of a cube based on the user-provided side length:

#include <iostream>
#include <cmath>

using namespace std;

int main() {
    double sideLength, surfaceArea, volume;

    // Input the side length of the cube
    cout << "Enter the side length of the cube: ";
    cin >> sideLength;

    // Calculating surface area and volume
    surfaceArea = 6 * pow(sideLength, 2);
    volume = pow(sideLength, 3);

    // Output the results
    cout << "Surface Area of the cube: " << surfaceArea << " square units" << endl;
    cout << "Volume of the cube: " << volume << " cubic units" << endl;

    return 0;
}
    

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Output

When the program is executed and a value for the side length is entered, it will compute the surface area and volume of the cube. Below is an example of the program's output:

Enter the side length of the cube: 4
Surface Area of the cube: 96 square units
Volume of the cube: 64 cubic units
    

In this example, the program calculates the surface area as 6 × 4² = 96 and the volume as 4³ = 64.

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Explanation

Let's break down the code to understand how it works:

• Header Files:
  • The program uses <iostream> for input and output operations like cin and cout.
  • The <cmath> library is included to use the pow() function for calculating squares and cubes.
• Input: The user is prompted to enter the side length of the cube. This value is stored in the variable sideLength.
• Calculations:
  • The surface area is calculated using the formula 6 × a². The pow(sideLength, 2) function computes a².
  • The volume is calculated using the formula a³. The pow(sideLength, 3) function computes a³.
• Output: The results are displayed using cout, with labels to indicate whether the value represents the surface area or volume.

This simple program effectively demonstrates how to use C++ for mathematical computations involving basic geometric shapes.

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Conclusion

The calculation of surface area and volume for a cube is a straightforward task when using C++. By implementing this program, you have learned how to:

• Use input/output functionality in C++ to interact with the user.
• Leverage the cmath library for mathematical operations.
• Apply geometric formulas to calculate surface area and volume.