Question

What is the output of the following \(\mathrm{C}++\) code? const double PI = 3.14159; double cylinderRadii[5] = {3.5, 7.2, 10.5, 9.8, 6.5}; double cylinderHeights[5] = {10.7, 6.5, 12.0, 10.5, 8.0}; double cylinderVolumes[5]; cout << fixed << showpoint << setprecision(2); for (int i = 0; i < 5; i++) cylinderVolumes[i] = 2 * PI * cylinderRadii[i] * cylinderHeights[i]; for (int i = 0; i < 5; i++) cout << (i + 1) << " " << cylinderRadii[i] << " " << cylinderHeights[i] << " " << cylinderVolumes[i] << endl;

Short answer

The output of the code is: 1 3.50 10.70 235.59 2 7.20 6.50 294.31 3 10.50 12.00 791.68 4 9.80 10.50 646.94 5 6.50 8.00 327.25

Step-by-step solution

Understand the Code

The code initializes three arrays: `cylinderRadii`, `cylinderHeights`, and `cylinderVolumes`, and a constant `PI`. It calculates cylinder volumes using a formula in a loop, and prints each cylinder's index, radius, height, and volume.

Determine Volume Formula

The formula for the volume in the code is given by \( V = 2 \times \pi \times \text{radius} \times \text{height} \). Here, instead of an actual cylinder volume, it calculates a value more related to the surface area (without the base and top).

Calculate Volumes

We calculate the volume for each cylinder using the given radii and heights with the formula: \( V = 2 \times 3.14159 \times R \times H \).- For radius 3.5 and height 10.7: \( V = 2 \times 3.14159 \times 3.5 \times 10.7 = 235.59 \)- For radius 7.2 and height 6.5: \( V = 2 \times 3.14159 \times 7.2 \times 6.5 = 294.31 \)- For radius 10.5 and height 12.0: \( V = 2 \times 3.14159 \times 10.5 \times 12.0 = 791.68 \)- For radius 9.8 and height 10.5: \( V = 2 \times 3.14159 \times 9.8 \times 10.5 = 646.94 \)- For radius 6.5 and height 8.0: \( V = 2 \times 3.14159 \times 6.5 \times 8.0 = 327.25 \)

Format and Print Output

The code uses `fixed << showpoint << setprecision(2)` to ensure each floating-point number is printed with two decimal places. The final output will print each index (from 1 to 5), followed by the corresponding cylinder's radius, height, and calculated volume.

Key concepts

C++ Loops

In C++, loops are a fundamental way to repeat a block of code multiple times. There are different types of loops available, such as `for`, `while`, and `do-while`. The `for` loop is particularly useful when the number of iterations is known in advance. It consists of three parts: initialization, condition, and increment.

In the given code, a `for` loop is used to iterate over arrays. The loop runs from 0 to 4 (inclusive), hence iterating 5 times. Each time, it calculates and stores a value in the `cylinderVolumes` array. The loop is defined as follows:
- **Initialization**: `int i = 0` declares the loop counter `i` and initializes it to 0.
- **Condition**: `i < 5` ensures the loop runs as long as `i` is less than 5.
- **Increment**: `i++` increases the value of `i` by 1 after each iteration.

This loop is beneficial when working with arrays, as it can easily iterate through all elements to perform calculations or actions.

Floating-point precision in C++

Floating-point numbers in C++ are used to represent non-integer numbers with decimal points. These floating-point values can cause precision issues due to their binary representation in memory. In computations where precision matters, we must carefully control the formatting of floating-point outputs.

In the example program, the code `fixed << showpoint << setprecision(2)` is used for precisely defining how floating-point numbers are displayed:
- **`fixed`**: This manipulator ensures the numbers are displayed in fixed-point notation.
- **`showpoint`**: It displays the decimal point even if there are no numbers after it, ensuring consistency in output.
- **`setprecision(2)`**: Limits the number of digits after the decimal point to two, providing precision and readability in the result.

Understanding floating-point manipulation is key when presenting numbers in C++, ensuring data is presented accurately to suit the requirements of your application.

Volume calculation in C++

Volume calculations in C++ involve using mathematical formulas to determine the space a 3D object occupies. However, understanding the formulas is crucial, especially when the context is slightly different from standard conventions, as seen in the cylinder calculation in the exercise.

Typically, the volume of a cylinder is calculated using the formula:
\[ V = \pi \times r^2 \times h \]
where \( r \) is the radius and \( h \) is the height. However, in this exercise, the formula used is more related to calculating twice the approximate surface area minus the top and bottom areas, which can lead to confusion. The formula used is:

\[ V = 2 \times \pi \times r \times h \]
This formula will result in different numeric values than what you would expect from a volume calculation.

When implementing such calculations in C++, using arrays to store geometry parameters and loop to iterate through calculations can be efficient. Always remember to check the requirement for either volume or surface area to ensure formulas align with your intended outcome.