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Area of Sectors and Lengths of Arcs

Area of Sectors and Lengths of Arcs. Basic Terminology. Central Angle : An angle in the center of a circle Arc: A portion of a circle. Arc. Basic Relationships. Arcs and Central Angles have the same measure. 65. 65. More Basic Terminology.

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Area of Sectors and Lengths of Arcs

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  1. Area of Sectors and Lengths of Arcs

  2. Basic Terminology Central Angle: An angle in the center of a circle Arc: A portion of a circle Arc

  3. Basic Relationships Arcs and Central Angles have the same measure. 65 65

  4. More Basic Terminology Major & Minor Arcs:Major arcs are between 180 and 360 degrees.Minor arcs are between 0 and 180 degrees. Naming Arcs: Minor arcs are named using 2 letters, while a major arc is named using 3 letters. This is done to avoid confusion. Minor Arc = AB Major Arc = ACB A Minor Arc B Major Arc C

  5. Let’s Practice Individually, we are going to work on P 390 (15-25 odd) T C 128 D B

  6. Finding the Length of an Arc Step 1: Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 5 cm Circumference = πd so… C= π(10)= 10π The arc takes up 90/360 degrees or ¼ of the circle.

  7. Finding the Length of an Arc Step 1: Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 120 240 8 cm We’re missing the angle in the red arc. Circumference = πd so… C= π(16)= 16π The arc takes up 120/360 degrees or 1/3 of the circle. pi form decimal form

  8. Finding the Length of an Arc Step 1: Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 130 4 cm Circumference = πd so… C= π(10)= 8π The arc takes up 130/360 degrees. I’m not sure what nice fraction that is. pi form decimal form

  9. Area of a Sector What is a sector? A sector is like a pizza slice. It is part of the area of a circle.

  10. Finding the Area of a Sector Step 1: Find the area of the entire circle (Area= πr2). Step 2: Figure out what fraction of the whole circle the sector takes up. (Hint: use 360) Step 3: Multiply the area by the fraction for the sector. 130 4 cm Area= πr2 so… Area= π42 =16π The sector takes up 130/360 degrees. I’m not sure what nice fraction that is. pi form decimal form

  11. Finding the Area of a Sector Step 1: Find the area of the entire circle (Area= πr2). Step 2: Figure out what fraction of the whole circle the sector takes up. (Hint: use 360) Step 3: Multiply the area by the fraction for the sector. 120 3 cm Area= πr2 so… Area= π32 =9π The sector takes up 240/360 degrees. pi form decimal form

  12. Finding the Area of Segments • What is a segment? The space between a line connecting two points of a circle and the circle itself.

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