Area of a circle

Definition

The area of a circle is the amount of space enclosed within its circumference. It is calculated using the formula $A = \pi r^2$, where $r$ is the radius of the circle.

5 Must Know Facts For Your Next Test

1. The formula for the area of a circle, $A = \pi r^2$, includes the constant $\pi$ (approximately 3.14159).
2. When given the diameter, the radius can be found by dividing it by 2, and then used to find the area.
3. Increasing or decreasing the radius of a circle has a quadratic effect on its area due to the $r^2$ term in the formula.
4. In problems involving polynomial functions, circles may appear in contexts requiring geometric interpretation or optimization.
5. Understanding how changes in a function's parameters affect geometric properties like area can be crucial for solving complex algebraic problems.

Review Questions

• What is the formula for calculating the area of a circle?
• How does doubling the radius of a circle affect its area?
• If given a diameter, how would you determine the radius to find the area?

Related terms

Radius: The distance from the center of a circle to any point on its circumference.

$\pi$ (Pi): A mathematical constant approximately equal to 3.14159 that represents the ratio of a circle's circumference to its diameter.

Diameter: A straight line passing through the center of a circle, connecting two points on its circumference; it is twice the length of the radius.