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Understanding Circles: Circumference, Area, Arc Length, and Sector Proportions

This lesson focuses on the properties of circles, including how to calculate the circumference and area using the diameter and radius. We will solve problems related to finding the radius of a circle from the area and explore the special properties of circles. Additionally, the lesson will cover how to calculate arc length and the area of sectors through proportional reasoning. Homework review and practice problems reinforce these concepts in a clear and engaging manner.

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Understanding Circles: Circumference, Area, Arc Length, and Sector Proportions

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  1. Warm-up • 1) Find the circumference and area of a circle with a diamater of 10 in. • 2) What would be the radius of a circle if it’s area is ? C = 31.42 in., A = 78..54 in.2 radius = 8

  2. Homework Review 2) 2 4) AB=16, DE=17 6) AB=32, DE=24 8) 6 10) RT=20, TV=16 12) RT=36, TV=27 14) 12 16) 18 28) 14.2 ft.

  3. Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How do we find arc length and area of sectors using proportions? Standard: MM2G3.c

  4. 6.7 Circumference and Arc Length

  5. Circumference Distance around the circle

  6. Circumference 2 p r = C or dp = C

  7. Find the circumference. 33 m 14.3 in. 103.7 m

  8. Arc Length Portion of the circumference A P B

  9. Find the circumference Find the arc length 5cm 3.82 m 50º 60º 22.92 m 4.36 cm

  10. Practice! Wkbk 6.7

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