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Area of a circle

from class:

Algebra and Trigonometry

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.

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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?

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