Question

Write a program to calculate the volume and surface area of a sphere from its radius, given as input. Here are some formulas that might be useful: \\[ \begin{array}{c} V=4 / 3 \pi r^{3} \\ A=4 \pi r^{2} \end{array} \\]

Short answer

Program reads radius, calculates, and outputs volume and surface area using given formulas.

Step-by-step solution

Understanding the Problem

We need to write a program that calculates the volume and surface area of a sphere given its radius as an input. We will use the formulas \( V=\frac{4}{3} \pi r^3 \) for volume and \( A=4 \pi r^2 \) for the surface area.

Define the Input

The program will need to take a single input, which is the radius \( r \) of the sphere. The input must be captured using a function or method suitable for reading numeric data in the programming language we are using.

Implement Volume Calculation

Using the formula for the volume, \( V=\frac{4}{3} \pi r^3 \), implement the calculation in the program. Be sure to import any necessary libraries for mathematical calculations, such as \( \pi \).

Implement Surface Area Calculation

Using the formula for the surface area, \( A=4 \pi r^2 \), implement the calculation in the program. Again, ensure any required mathematical constants like \( \pi \) are available for use.

Display the Results

Once both the volume and surface area have been calculated, write code to display or return these values clearly to the user.

Key concepts

Programming a Sphere Calculator

Creating a program to calculate the volume and surface area of a sphere can be a fun and educational way to understand basic programming concepts. In this exercise, we need a program that computes these two properties of a sphere using its radius as input. Since these calculations involve mathematical operations, such as exponents and constants like \( \pi \), programming allows us to efficiently automate the task and handle complex calculations.

Generally, a programming task involves collecting inputs, processing these inputs through the logic of mathematics, and outputting the results. Here's a quick roadmap:

• Define the problem and identify the needed calculations.
• Break down the problem into logical steps for ease of implementation.
• Choose a suitable programming language (Python in this instance) and start coding!

By following structured steps, such as defining inputs, implementing calculations, and displaying outputs, programming helps solve mathematical problems systematically.

Understanding Mathematical Formulas

Mathematics provides the foundation for programming when it comes to calculations like volume and surface area of solids. For a sphere, the key formulas are:

* Volume, \( V = \frac{4}{3} \pi r^3 \): This formula tells us how much space is inside the sphere. It involves cubing the radius, which means multiplying the radius by itself twice more, and then multiplying by \( \pi \) and \( \frac{4}{3} \).
* Surface Area, \( A = 4 \pi r^2 \): This formula calculates the total area that the surface of the sphere occupies. It requires squaring the radius, which means multiplying the radius by itself, and then multiplying by \( 4 \pi \).

These formulas are derived from geometry, where \( \pi \) (pi) is a constant that represents the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. By applying these formulas, we can get precise calculations of a sphere's volume and surface area without manually measuring them.

Implementing with Python Programming

Python is an excellent choice for writing a program to calculate a sphere's volume and surface area because it is simple and powerful for handling mathematical computations. To implement this, you'll need to work with several key aspects of Python programming.

**Importing Libraries:** Python provides a 'math' library that includes the constant \( \pi \), which simplifies mathematical calculations. It can be imported using the line `import math`.

**Reading Input:** Use the `input()` function to get the radius from the user. Ensure the input is converted to a floating-point number using `float()` for accurate calculations: `radius = float(input("Enter the radius: "))`.

**Calculating Volume and Surface Area:** Using the formulas discussed: * Volume: `volume = (4/3) * math.pi * radius**3` * Surface Area: `surface_area = 4 * math.pi * radius**2`

**Displaying Results:** Finally, use the `print()` function to display the results, formatting the output for clarity, such as `print(f"Volume: {volume}, Surface Area: {surface_area}")`.

By utilizing these functions and structures, Python simplifies the process of connecting mathematical formulas to real-world applications in a user-friendly way.