Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of.

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Presentation transcript:

Geometry 1 Area and Circumference of a Circle

Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of a minor arc is the measure of its central angle. The measure of a major arc is 360 minus the measure of its central angle. The arc measure is written as

Circumference Example: Example:Find the circumference of the following circle. 3 cm cm When finding the circumference of a circle, you can leave your answer in terms of pi.

Circumference: Circumference is the distance around the circle. 4 Formula:Or Example:Find the circumference of the following circle. 3 cm cm where

Example: If a bicycle tire has a diameter of 26 inches, how far does it travel in 1000 revolutions of the tire? Use Example: The rim of a satellite dish has a diameter of 7 feet. Find the circumference of the rim and the area of the circle defined by the rim. Use 3.14.

Example: A Ferris wheel has diameter of 42 feet. How far will a rider travel during a 4 minute ride if the wheel rotates once every 20 seconds? Use 22/7. Example: The tires of a racing bike are approximately 70 cm in diameter. How far does a bike racer travel in 5 minutes if the wheels are turning at a speed of 3 revolutions per second? How many revolutions does a wheel make in 22 km race? Use 22/7.

Area of a Circle Area of a circle is the number of unit squares that can fit into a circle. 7 Example:Find the area of the following circle. 3 cm Formula:

Complete the table below and leave your answers in terms of pi. Radius8 Diameter Circumference26π Area18π