Area of a Circle: Formulas and Examples

The transcript provides a comprehensive overview of calculating the area of a circle using various methods and examples. It covers key concepts and formulas related to circular geometry.

• The fundamental formula for the area of circle with radius r is A = πr²
• Several examples demonstrate how to apply this formula in different scenarios
• The relationship between diameter and radius (d = 2r) is utilized in calculations
• Practical applications include finding shaded areas and solving for unknown variables

Definition: The area of a circle is the amount of space enclosed within its circumference, calculated using the formula A = πr², where r is the radius.

Highlight: Understanding how to manipulate the area formula is crucial for solving various types of circular area problems.

The transcript includes five detailed examples:

1. Finding the area of a circle with a given diameter
2. Calculating the radius when the area is known
3. Determining the area of a circle inscribed in a square
4. Computing the area of a shaded region between a square and an inscribed circle
5. Finding the diameter of a circle with a specified area

Example: For a circle with a diameter of 12 cm, the area is calculated as A = π(6²) = 36π cm², approximately 113.1 cm².

Vocabulary:

• Radius: The distance from the center of a circle to its edge
• Diameter: The length of a line through the center of a circle from one side to the other, equal to twice the radius

The document also mentions Quizizz codes for classwork and homework, suggesting interactive practice opportunities for students to reinforce their understanding of circular area calculations.

Highlight: Practice and application are key to mastering the concepts of circular area calculations, as evidenced by the multiple examples and practice opportunities provided.