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Circles

In this topic, we will learn the concept of area and circumference of circles. We will also learn about the sectors of the circle and the application problems based on it.

Topic: Circumference of Circles

  • Circumference of a circle (C)= 2∏r or ∏d

  • r = C/2∏; d = C/∏

  • The distance traveled by a wheel in one complete revolution (turn) is equal to the circumference of the wheel

Topic: Area and Sector of Circles

  • Area of a circle = ∏ x r2

  • A sector of a circle is a portion of the interior of the circle enclosed by the two radii and an arc which is part of the circle

  • The angle formed by the radii, called the central angle (q), determines the
    fraction of the area of the circle the sector occupies

  • Area of the sector = (q/360) x ∏r2

  • Circumference of the arc = (q/360) x 2∏r
                                            = (q/360) x ∏d

Topic: Area and Circumference on a Coordinate Plane

  • The radius of the circle is the distance between the center and the point through which it passes

  • Area of the circle = ∏r2

  • Perimeter of the circle = 2∏r or ∏d

Topic: Area and Perimeter of Complex Figures

  • A complex figure is the figure that is made of more than one shape

  • The area of a complex figure is calculated by adding/subtracting the area of the figures that form the complex figure
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