91Ó°ÊÓ

To find the area of a circle, you use the formula: \[\text{Area} = \pi r^2\]. This formula requires two main components: \(\text{pi}\) and the radius (\(r\)). The symbol \(\text{pi}\) (Ï€) represents a constant that is used in mathematics to relate the circumference of a circle to its diameter. It is approximately equal to 3.14. The radius (\(r\)) is the distance from the center of the circle to any point on its boundary. Understanding and correctly applying this formula is crucial in geometry. For example, in our exercise, the radius was determined to be 6 meters. When we substitute this into the formula, it helps us find the area efficiently.

The radius and diameter of a circle have a direct relationship. The diameter is twice the length of the radius. This means if you know the diameter, you can easily find the radius by dividing the diameter by two. In our given problem, we had a circle with a diameter of 12 meters. By dividing this diameter by two, \(d/2\), we find that the radius \(r\) is \(12/2 = 6 \text{ m}\). This step is essential because the radius is used in the circle area formula.

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. Pi is an irrational number, meaning it has an infinite number of decimal places and doesn't repeat. For most practical purposes, we use the approximation \(\pi ≈ 3.14\). This simplifies calculations and is accurate enough for many uses. However, in some cases, you might use a more accurate approximation like \(\pi ≈ 3.14159\), or use the symbol π itself in equations involving circles. In our problem, we use \(\pi ≈ 3.14\) for finding the area. By multiplying \(π\) with the squared radius value (36), you get: \(3.14 \times 36 = 113.04 \text{ m}^{2}\). This gives us the area of the circle.