8.2. Areas of Circles and Sectors For use with Exploration 8.2. Essential Question How can you find the area of a sector of a circle?

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1 8.2 Areas of Circles and Sectors For use with Exploration 8.2 Essential Question How can ou find the area of a sector of a circle? 1 EXPLORATION: Finding the Area of a Sector of a Circle Work with a partner. A sector of a circle is the region bounded b two radii of the circle and their intercepted arc. Find the area of each shaded circle or sector of a circle. a. entire circle b. one-fourth of a circle x 8 x c. seven-eighths of a circle d. two-thirds of a circle x x 295 Copright Big Ideas Learning, LLC

2 _ 8.2 Areas of Circles and Sectors (continued) 2 EXPLORATION: Finding the Area of a Circular Sector Work with a partner. A center pivot irrigation sstem consists of 00 meters of sprinkler equipment that rotates around a central pivot point at a rate of once ever 3 das to irrigate a circular region with a diameter of 800 meters. Find the area of the sector that is irrigated b this sstem in one da. Communicate Your Answer 3. How can ou find the area of a sector of a circle?. In Exploration 2, find the area of the sector that is irrigated in 2 hours. Copright Big Ideas Learning, LLC 296

3 8.2 Notetaking with Vocabular For use after Lesson 8.2 In our own words, write the meaning of each vocabular term. geometric probabilit sector of a circle Core Concepts Area of a Circle The area of a circle is r A = π r 2 where r is the radius of the circle. Notes: 297 Copright Big Ideas Learning, LLC

4 _ 8.2 Notetaking with Vocabular (continued) Area of a Sector The ratio of the area of a sector of a circle to the area of the whole circle ( πr 2 ) is equal to the ratio of the measure of the intercepted arc to 360. Area of sector APB 2 π r Area of sector APB mab =,or 360 mab = π r P r A B Notes: Extra Practice Practice A In Exercises 1 2, find the indicated measure. 1. area of 2. area of R 7 m 5 cm R In Exercises 3 8, find the indicated measure. 3. area of a circle with a diameter of 1.8 inches. diameter of a circle with an area of 10 square feet Copright Big Ideas Learning, LLC 298

5 8.2 Notetaking with Vocabular (continued) 5. radius of a circle with an area of 65 square centimeters 6. area of a circle with a radius of 6.1 ards 7. areas of the sectors formed b PQR 8. area of Y P cm 10 R Q Y 25 Z X A =.1 square feet 9. You throw a dart at the board shown. Your dart is equall likel to hit an point inside the square board. a. What is the probabilit our dart lands in the smallest triangle? b. What is the probabilit our dart does not land anwhere in the circle? Copright Big Ideas Learning, LLC

6 Practice 11.2 BPractice B In Exercises 1, find the indicated measure. 1. area of a circle with a radius of 6.75 inches 2. area of a circle with a diameter of 3 10 mile 3. radius of a circle with an area of 63.7 square kilometers. diameter of a circle with an area of square ards In Exercises 5 8, find the areas of the sectors formed b JL J 8. 5 J 2.9 cm in m L J 113 L L d L 77 J 9. Find the radius of H. 10. Find the radius of. A =.8 cm 2 F E 88 H G J 25 L A = 1.05 ft 2 In Exercises 11 13, find the area of the shaded region m ft 6 in. in. 1. A tire is hung from a tree. The outside diameter is 3 inches and the inside diameter is 1 inches. You throw a baseball toward the opening of the tire. Your baseball is equall likel to hit an point on the tire or in the opening of the tire. What is the probabilit that ou will throw the baseball through the opening in the tire? Copright Big Ideas Learning, LLC 300

11.2 Areas of Circles and Sectors

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