Arc Lengths and Sectors Unit 6-3. Finding the length of Arcs An arc is part of the circumference of a circle, so you will use the circumference formula.

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Presentation transcript:

Arc Lengths and Sectors Unit 6-3

Finding the length of Arcs An arc is part of the circumference of a circle, so you will use the circumference formula to find the length of arcs. Arc length = the part of Circumference

Finding the Area of Sectors A sector is part of the area of a circle, so you will use the area formula to find the area of the sector.

Finding the Area of Segments A segment is part of the area of a circle. You will find the area of the entire sector, then subtract out the area of the triangle. Area of the sector minus area of the triangle

Arc Length Example -- 1 D H T Find the length of arc DT 85 o 4.2

Arc Length Example -- 2 D H T Find the length of arc DT 110 o 6

Sector Area Examples--1 D H T Find the area of the sector 110 o 6 cm

Sector Area Examples--2 D H T Find the area of the sector 14 o 5.7 m

Segment Area Examples--1 D H Find the area of the segment 270 o 11 in R

Segment Area Examples--2 D H Find the area of the segment 240 o HD = 8 ft DF = 20 ft F

Word Problems A circle has an arc length of The central angle is 55 degrees, find the diameter.

Word Problems A circular plot with a 720 ft diameter is watered by a spray irrigation system. To the nearest square foot, what is the area that is watered as the sprinkler rotates through an angle of 50 o