Question

Here's a peek ahead. In this chapter, you learned about integers and the type int. Java can also represent floating-point numbers that contain decimal points, such as \(3.14159 .\) Write an application that inputs from the user the radius of a circle as an integer and prints the circle's diameter, circumference and area using the floating-point value 3.14159 for \(\pi .\) Use the techniques shown in Fig. \(2.7 .[\) Note: You may also use the predefined constant Math.PI for the value of \(\pi\). This constant is more precise than the value \(3.14159 .\) Class Math is defined in package java. Tang. Classes in that package are imported automatically, so you do not need to import class Math to use it.] Use the following formulas ( \(r\) is the radius): diameter \(=2 r\) circumference \(=2 \pi r\) area \(=\pi r^{2}\) Do not store the results of each calculation in a variable. Rather, specify each calculation as the value that will be output in a System.out.printf statement. The values produced by the circumference and area calculations are floating-point numbers. Such values can be output with the format specifier \%f in a System.out.printf statement. You'll learn more about floating-point numbers in Chapter 3.

Short answer

Prompt for the radius, directly calculate and print the diameter (2 * radius), circumference (2 * Math.PI * radius), and area (Math.PI * radius * radius) using System.out.printf with appropriate format specifiers.

Step-by-step solution

Read the user Input

Prompt the user to enter the radius of the circle as an integer. Use the Scanner class to read the user input and store it in an int variable named 'radius'.

Calculate the Diameter

Use the formula diameter = 2 * radius to calculate the diameter of the circle. Directly include this calculation in the print statement, without storing it in a separate variable.

Calculate the Circumference

Use the formula circumference = 2 * Math.PI * radius to calculate the circumference of the circle. As with the diameter, include this calculation in the print statement directly.

Calculate the Area

Using the formula area = Math.PI * radius * radius, calculate the area of the circle. Same as before, include this calculation in the print statement without storing it in a variable.

Display the Results

Use System.out.printf to output the calculated diameter, circumference, and area to the console. Use '%d' as the format specifier for an integer, and '%f' for floating-point numbers.

Key concepts

Java floating-point numbers

When you're working with Java, understanding floating-point numbers is crucial, especially in calculations involving precision, such as those with circle dimensions. In Java, floating-point numbers are numbers that have a decimal point and can represent fractions, much like the real numbers in math. There are two primary data types for floating-point numbers: float, which is a single-precision 32-bit IEEE 754 floating point, and double, which is a double-precision 64-bit IEEE 754 floating point.

For many calculations, double will be preferred because of its larger range and greater precision. For instance, the constant 3.14159 used to represent \(\pi\) is a floating-point number that can be better represented by Math.PI, which is a double. When calculating a circle's properties, using double ensures that the results are as accurate as possible, given the limitations of representing real numbers in a computer's binary system.

It's essential to note that floating-point numbers are an approximation. Because of this, rounding errors can occur, so when it's vital to have precise results, as in financial calculations, other data types, like BigDecimal, might be more appropriate. But for our circle calculations, the precision of double and the use of Math.PI will offer the accuracy we need to output reasonably exact dimensions.

System.out.printf usage

The System.out.printf method is a powerful tool in Java for formatting and printing strings to the console. It allows developers to create sophisticated output with placeholders for data, known as format specifiers, that represent different types of data like integers, floating-point numbers, and strings.

In the context of printing the properties of a circle, System.out.printf lets you directly calculate and insert values into a string. The '%d' format specifier stands for a decimal integer, while '%f' is used for floating-point numbers. For instance, when you calculate the circle's area, you can use '%f' to include the floating-point result directly into the output string. A handy feature of System.out.printf is that it allows for the control of the precision of the floating-point number by specifying the number of decimal places, like '%.2f' for two decimal places.

This method grants not just effective output, but also readability in the code, by keeping calculations and print statements concise. It's this combination of precision control and clarity that makes System.out.printf an excellent choice for displaying calculated results, such as those found in our circle dimensions example.

Math.PI constant

One cannot talk about circle calculations without acknowledging the significance of \(\pi\), an essential mathematical constant. In Java, \(\pi\) is provided as Math.PI. This is a built-in constant representing the ratio of the circumference of a circle to its diameter, which is approximately 3.14159, but much more precise as a double value provided in the Math class.

Why is this precision important? When you're calculating the circle's diameter, circumference, or area, using Math.PI provides a much closer approximation to the true values than using a truncated version of \(\pi\). Precise calculations are particularly vital in scientific and engineering contexts where the accuracy of results is paramount.

Using Math.PI not only offers better precision but also simplifies the code. There's no need to manually enter the value of \(\pi\) when it's readily available and more accurate through this constant. By incorporating Math.PI into our formulas, as seen in the circle calculations exercise, we improve the accuracy of the program's output and adhere to the best coding practices in Java.