Geometry Honors Section 5.3 Circumference and Area of Circles.

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Presentation transcript:

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

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 _____

Once again, =, so C = ____ or in terms of the radius C = ______

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

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 1000 th.

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

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

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

Example: Find the area of sector AQB.

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

Example: A circle has a diameter of 30 feet. If the area of a sector in this circle has a measure of ft 2, find the measure of arc determining this sector.

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

Example: A circle has a radius of 6 cm. If an arc has a measure of 80 0, find the length of the arc.

Example: An arc has a measure of 30 0 and a length of inches. What is the radius of the circle in which this arc is found?

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.

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.

A radian is a unit of angle measure

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

Example: Convert 72 o to radians

Example: Convert radians to degrees