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Geometry Honors Section 5.3 Circumference and Area of Circles

Geometry Honors Section 5.3 Circumference and Area of Circles. While the distance around the outside of a polygon is known as the ________, the distance around the outside of a circle is called the ____________. perimeter. circumference.

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Geometry Honors Section 5.3 Circumference and Area of Circles

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  1. Geometry Honors Section 5.3Circumference and Area of Circles

  2. While the distance around the outside of a polygon is known as the ________, the distance around the outside of a circle is called the ____________. perimeter circumference

  3. For any circle, the ratio of the circumference to the diameter, , is the same. This ratio is approximately equal to ___________. We use the Greek letter ____ to represent this irrational number. A fractional approximation is _____. 3.141592656

  4. Once again, = , so C= ____or in terms of the radius C= ______

  5. Activity 2 on page 316 explains how the formula for the area of a circle is derived. A = ______

  6. Example: Find the circumference and area of a circle with a diameter of 12. Give an exact answer and an answer rounded to the nearest 1000th.

  7. Example: Find the area of a circle with a circumference of .

  8. Example: Find the area of the shaded region. Give an exact answer and an answer rounded to the nearest 1000th.

  9. A sector of a circle is the region bounded by two radii and the arc joining there outer endpoints.

  10. Example: Find the area of sector AQB.

  11. As you can see from the previous example, the area of a sector = OR

  12. Example: A circle has a diameter of 30 feet. If the area of a sector in this circle has a measure of ft2, find the measure of arc determining this sector.

  13. A similar formula can be used to find the length of an arc. Length of an arc = OR

  14. Example: A circle has a radius of 6 cm. If an arc has a measure of 800, find the length of the arc.

  15. Example: An arc has a measure of 300 and a length of inches. What is the radius of the circle in which this arc is found?

  16. Note: The “measure of an arc” and the “length of an arc” are not the same thing. The measure of an arc is given in _______ and refers to ___________________ The length of an arc is given in __________ and refers to _______________________ degrees a fraction of the circle. in / cm / ft the distance along the arc.

  17. While degree is certainly the unit of angle measure that you are most familiar with, another commonly used unit for measuring angles is the radian.

  18. A radian is a unit of angle measure

  19. Since the circumference of any circle is equal to ______, then there must be _____ arcs of length ___ on any circle. Thus, the radian measure of a full circle is _____. We also know the degree measure of a full circle is _______. Therefore, _______________________or

  20. Example: Convert 72o to radians

  21. Example: Convert radians to degrees

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