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Chapter 4: Problem 30

\(\quad\) (Calculating a Circle's Diameter, Circumference and Area) Write a program that reads the radius of a circle (as a double value) and computes and prints the diameter, the circumference and the area. Use the value 3.14159 for \(\pi\)

Short Answer

Expert verified
To calculate the diameter, double the radius. The circumference is \(2 \times \text{Radius} \times \text{pi}\), and the area is \( \text{pi} \times \text{Radius}^2\).

Step by step solution

01

Understand the Circle Properties

To solve the exercise, recall the basic properties of a circle. The diameter is twice the radius, the circumference is the distance around the circle and is calculated with the formula \(2 \times \text{radius} \times \text{pi}\), and the area is the space contained within the circle, given by \( \text{pi} \times \text{radius}^2\). Use \( \text{pi}=3.14159\) as provided.
02

Read the Circle's Radius

Read the circle's radius (provided by the user or the given problem) and store it in a variable. Ensure that the value is read as a double to allow for decimal precision.
03

Calculate the Diameter

Multiply the radius by two to calculate the diameter. The formula is \( \text{Diameter} = 2 \times \text{Radius}\).
04

Calculate the Circumference

Use the formula \( \text{Circumference} = 2 \times \text{pi} \times \text{Radius}\) to calculate the circumference.
05

Calculate the Area

Calculate the area using the formula \( \text{Area} = \text{pi} \times \text{Radius}^2\).
06

Print the Results

Output the calculated diameter, circumference, and area, making sure to label each value so the user can understand the displayed numbers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Circle Diameter Calculation
Understanding the diameter of a circle is key in the realm of geometry. In simple terms, the diameter is the straight line that passes through the center of the circle and touches two points on its edge. Computationally, if you know the radius—which is half of the diameter—you can easily double that value to find the diameter. In C++, assuming you've already prompted the user to input the radius and stored that input into a variable named radius, the calculation would look something like this: double diameter = 2 * radius;.

When creating a program to calculate the diameter, it's always a good practice to use constants for any fixed values. While in this exercise, the value of \( \pi \) is provided as 3.14159, we actually do not need \( \pi \) when calculating the diameter, as it's a direct multiple of the radius. Always ensure the correct data type is used to maintain precision—in this case, double is appropriate for the radius and diameter.
Circle Circumference Formula
Moving on to the circumference, which is the perimeter or the distance around a circle, the formula to calculate it is straightforward: \( \text{Circumference} = 2 \times \pi \times \text{Radius} \). The circumference can be thought of as the total distance one would travel if they walked around the circle's edge once.

In a C++ program, you would use this formula after obtaining the radius from the user. The calculation might appear as follows: double circumference = 2 * 3.14159 * radius;. Remember to use the constant value of \( \pi \) provided in the problem statement. If the program required more precision or if \( \pi \) were used in multiple calculations, defining \( \pi \) as a constant at the beginning of the program would be beneficial. For instance: const double PI = 3.14159; and then using PI in your calculation to enhance readability and maintainability of the code.

It's essential to convey to students that using constants can prevent errors if the value of the constant needs to be changed later, it can be done in one place rather than throughout multiple lines of code.
Circle Area Computation
Lastly, the area of a circle is the amount of space it occupies on a two-dimensional plane. You can calculate the area with the formula \( \text{Area} = \pi \times \text{Radius}^2 \).

In C++, after reading the radius, you can compute the area similarly to how we've computed the diameter and circumference. The code for this calculation would be: double area = PI * radius * radius;, where PI is the constant for \( \pi \) we've defined earlier. It's critical to square the radius, which means multiplying the radius by itself; this is a common mistake when learners are new to programming and mathematics.

It's also worth noting the importance of explaining to students why the area is related to the square of the radius rather than just the radius. The reason is because area is a measure of a two-dimensional space, and squaring the radius indicates that we're considering the radius in both dimensions of the plane. This is a fundamental concept in the computation of areas for all shapes, not just circles. Furthermore, ensuring that students understand the relationship between the formulas for diameter, circumference, and area can provide them with a deeper understanding of geometry and its applications in coding.

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Most popular questions from this chapter

(Square of Asterisks) Write a program that reads in the size of the side of a square then prints a hollow square of that size out of asterisks and blanks. Your program should work for squares of all side sizes between 1 and \(20 .\) For example, if your program reads a size of \(5,\) it should print ***** * * * * * * *****

\((\text { Multiples of } 2\) with an Infinite Loop) Write a program that prints the powers of the integer \(2,\) namely \(2,4,8,16,32,64,\) etc. Your while loop should not terminate (i.e., you should create an infinite loop). To do this, simply use the keyword true as the expression for the while statement. What happens when you run this program?

(Dangling-else Problem) State the output for each of the following when \(x\) is 9 and \(y\) is 11 and when \(x\) is 11 and \(y\) is \(9 .\) The compiler ignores the indentation in a \(C++\) program. The \(C++\) compiler always associates an else with the previous if unless told to do otherwise by the placement of braces \\{\\}\(.\) On first glance, you may not be sure which if and else match, so this is referred to as the "dangling-else" problem. We eliminated the indentation from the following code to make the problem more challenging. [Hint: Apply indentation conventions you've learned.] (Dangling-else Problem) State the output for each of the following when \(x\) is 9 and \(y\) is 11 and when \(x\) is 11 and \(y\) is \(9 .\) The compiler ignores the indentation in a \(C++\) program. The \(C++\) compiler always associates an else with the previous if unless told to do otherwise by the placement of braces \\{\\}\(.\) On first glance, you may not be sure which if and else match, so this is referred to as the "dangling-else" problem. We eliminated the indentation from the following code to make the problem more challenging. [Hint: Apply indentation conventions you've learned.]

\(4.26 \quad\) forward. For example, each of the following five-digit integers is a palindrome: 12321,55555 45554 and \(11611 .\) Write a program that reads in a five-digit integer and determines whether it's a palindrome. [Hint: Use the division and modulus operators to separate the number into its individual digits.

include 4 using name… # (What Does this Program Do?) What does the following program print? 1 // Exercise 4.22: ex04_22.cpp 2 // What does this program print? 3 #include 4 using namespace std; 5 6 int main() 7 { 8 int row = 10; // initialize row 9 int column; // declare column 10 11 while ( row >= 1 ) // loop until row < 1 12 { 13 column = 1; // set column to 1 as iteration begins 14 15 while ( column <= 10 ) // loop 10 times 16 { 17 cout << ( row % 2 ? "<" : ">" ); // output 18 ++column; // increment column 19 } // end inner while 20 21 --row; // decrement row 22 cout << endl; // begin new output line 23 } // end outer while 24 } // end main
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