Question

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 \(p\).

Short answer

Declare variables, read radius, calculate diameter as \(2\times \text{radius}\), and calculate circumference using \(2\pi\times \text{radius}\).

Step-by-step solution

Declare Variables

Start by declaring the variables needed in the program. You will need a double variable for the radius (input by the user) and three additional doubles to store the calculated diameter, circumference, and area of the circle. Additionally, declare a constant for the value of π (pi) as 3.14159.

Read User Input

Prompt the user to input the radius of the circle. Use a scanner object or any other standard input method in the programming language to read the user's input and store it in the variable declared for the radius.

Calculate the Diameter

The diameter of a circle is twice its radius. Compute this by multiplying the radius by 2. Store the result in the variable reserved for the diameter: \[ \text{diameter} = 2 \times \text{radius} \]

Calculate the Circumference

The formula to calculate the circumference of a circle is \(2πr\), where \(r\) is the radius. Use the constant π and the radius provided by the user to calculate: \[ \text{circumference} = 2 \times 3.14159 \times \text{radius} \]

Key concepts

Radius of a Circle

The radius is the distance from the center of the circle to its edge. It's a key measurement in circle geometry, as it helps us find other important properties of a circle, such as the diameter, circumference, and area.

• The radius is always half the length of the diameter. If you know the diameter, you can quickly find the radius by dividing it by 2.
• When solving problems, the radius is often the starting point for calculations, making it essential for anyone learning geometry.

In programming exercises, you'll often be asked to input the radius first before performing any calculations. This gives you the foundation you need to figure out all the other characteristics of the circle.

Diameter Calculation

Finding the diameter of a circle is straightforward once you know the radius. The diameter is the longest straight line you can draw across a circle, passing through its center.

• The diameter is twice the length of the radius, expressed as: \[ \text{diameter} = 2 \times \text{radius} \]
• This calculation is intuitive and quick, making diameter one of the easiest circle measurements to find.

Always remember that because the diameter passes through the center, it is a key part of understanding and drawing circles in geometry. By doubling the radius, you get a clear picture of the circle's full width.

Circumference Formula

The circumference is the total distance around a circle, similar to the perimeter of other shapes. To find this measurement, we use the radius and the well-known mathematical constant π (pi).

• The formula for circumference is: \[ \text{circumference} = 2 \pi \times \text{radius} \]
• In many exercises, π is taken as 3.14159, ensuring more accurate calculations.

This formula underlines the relationship between linear distances (like the diameter and radius) and π, which represents the ratio of a circle's circumference to its diameter. Calculating the circumference is a practical application in various fields, including engineering and construction.

Area Calculation

The area of a circle refers to the total space within its boundary. Knowing how to calculate it is crucial in many practical and theoretical applications. The area depends on the radius of the circle.

• The formula to find the area is: \[ \text{area} = \pi \times \text{radius}^2 \]
• Squaring the radius means multiplying it by itself, emphasizing the exponential nature of area calculations in circle geometry.

Understanding this formula helps in real-world applications, such as determining space requirements for round tables or circular gardens. By mastering area calculations, you can apply mathematical concepts more effectively in everyday situations.