Welcome! Today we'll learn how to find the area of a circle. The area of a circle represents the amount of space contained within the circle's boundary. We can see a circle here with its radius marked in red.
The area of a circle is calculated using the formula A equals pi r squared. In this formula, A represents the area, pi is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. This formula tells us that the area is proportional to the square of the radius.
Now let's work through a step-by-step example. Suppose we have a circle with radius equal to 3 units. First, we identify the radius as 3. Second, we square the radius: 3 squared equals 9. Third, we multiply by pi: A equals 9 pi. Finally, we get approximately 28.27 square units.
Let's see how the radius affects the area. Notice that when we double the radius from 1 to 2, the area doesn't just double - it quadruples! This is because we square the radius in our formula. When the radius is 1, the area is about 3.14. When the radius becomes 2, the area becomes about 12.57, which is four times larger.
Let's summarize what we've learned about finding the area of a circle. The key formula is A equals pi r squared. Remember that the area depends on the radius squared, so doubling the radius quadruples the area. Pi is approximately 3.14159, and area units are always squared. Here are three practice examples with different radii to help you practice the calculation.