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 area formula $A = \pi r^2$ directly relates to power functions, specifically quadratic functions.
2. Understanding how to manipulate and simplify expressions involving $\pi$ and $r$ is crucial for solving related algebraic problems.
3. In polynomial terms, $\pi r^2$ represents a monomial with a degree of 2.
4. Problems often require converting diameter to radius; recall that the radius is half of the diameter: $r = \frac{d}{2}$.
5. Applications may involve solving for $r$ or $\pi$, requiring skills in isolating variables and handling square roots.

Review Questions

• What is the formula for calculating the area of a circle, and what does each variable represent?
• How would you express the area of a circle as a polynomial function?
• If given the diameter instead of the radius, how do you adjust your calculation for the area?

Related terms

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

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

Quadratic Function: A polynomial function with a degree of two, typically in the form $ax^2 + bx + c$.