11. AREAS RELATED TO CIRCLES

11. AREAS RELATED TO CIRCLES

  • 11

    Areas Related To Circles

    This section discusses the concepts of sectors and segments of circles, detailing their areas and the formulas to calculate them.

  • 11.1

    Areas Of Sector And Segment Of A Circle

    This section explores the definitions, formulas, and calculations related to the areas of sectors and segments of circles.

  • 11.2

    Summary

    This section outlines the essential formulas for calculating the length of an arc and the area of a sector and segment of a circle.

    • Key Summary

    The chapter covers the concepts of sectors and segments of a circle, including the formulas needed to calculate their areas and the lengths of arcs. It provides detailed explanations of how to derive the area of a sector based on its angle and radius, and also discusses the relationship between the areas of segments and their corresponding triangles. Various examples reinforce the application of these concepts in solving problems relevant to circles.

    Key Takeaways

    • Length of an arc of a sector of a circle with radius r and angle with degree measure θ is θ/360 × 2πr.
    • Area of a sector of a circle with radius r and angle with degree measure θ is θ/360 × πr².
    • Area of a segment of a circle = Area of the corresponding sector - Area of the corresponding triangle.

    Key Concepts

    • Sector: A sector of a circle is a portion enclosed by two radii and the arc between them.
    • Segment: A segment of a circle is the area enclosed by a chord and the arc connecting the endpoints of the chord.
    • Arc Length: The distance along the arc connecting two points on the circle, calculable using the arc's angle and radius.
    • Area of Sector: The area of a sector can be calculated using the formula (θ/360) × πr².