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Keystone Geometry

Arc Length and Area of a Sector. Keystone Geometry. Sector of a Circle.

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Keystone 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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