Welcome to our exploration of the area of a circle. The area of a circle represents the total amount of space enclosed within the circle's boundary. Think of it as how much surface the circle covers, like the amount of paint needed to fill in a circular shape completely.
The area of a circle is calculated using the formula A equals pi times r squared. Here, A represents the area, pi is a mathematical constant approximately equal to three point one four one five nine, and r is the radius of the circle. The radius squared means we multiply the radius by itself.
Let's work through a step-by-step example. Consider a circle with radius equal to 3 units. First, we square the radius: 3 squared equals 9. Next, we multiply by pi: area equals pi times 9, which is 9 pi. Finally, we calculate the numerical value: 9 times 3.14 equals approximately 28.26 square units.