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Understanding Arc Length and Area of a Sector in Circle Geometry

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This guide explores the concepts of arc length and area of a sector in circle geometry. A sector is defined as a region bounded by two radii and an arc. The area of a sector is a fraction of the total area of the circle, while the arc length is determined by the central angle and circumference of the circle. Formulas and examples are provided for calculating arc length and sector area, including practical applications like paper fans and window wipers. Learn how to apply these concepts through real-world scenarios and examples.

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Understanding Arc Length and Area of a Sector in Circle Geometry

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  1. Arc Length and Area of a Sector Keystone Geometry

  2. Sector of a Circle A sector of a circle is a region bounded by two radii and an arc of the circle. The area of the sector is a fraction of the area of a circle. The arc length that bounds the sector is a fraction of the circumference of the circle.

  3. Arc Length Arc length is the distance around an arc . Formula: The circumference multiplied by the ratio of the center angle and 360º. Example: Arc Length

  4. A ° 72 B 4 cm C Example Example: Find the Arc Length of AC if the central angle is 72 degrees and circle B has a radius of 4 cm.

  5. Paper Fans • In the green fan, find the length of arc CD • In the red fan, find the length of arc EF • In the blue fan, find the length of arc AB

  6. Tires

  7. Area of a Sector Area of a sector is the area of a section of the circle. It is a fraction of the entire area that is dependent upon the size of the central angle. Formula: The area multiplied by the ratio of the center angle and 360° Example: Sector

  8. Example Example: Find the area of a sector if the Central angle is 65 degrees and the radius of the circle is 3 cm. Example: Sector 65°

  9. Paper Fan • A stretched out paper fan forms a sector with a radius of 18 cm and an angle of 175⁰. Calculate the area of the stretched out fan. Give your answer to 1 decimal place.

  10. Windshield Wipers • A window wiper of length 20 inches goes through an angle of 160⁰. Work out the area of window covered by the window wiper.

  11. A A 60 6 4 Find the area of the shaded region. Point M marks the center of a circle. Leave your answers in terms of Pi. M M

  12. Round each answer to the nearest tenth.

  13. Round each answer to the nearest tenth.

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