11.2 Start Thinking Warm Up Cumulative Review Warm Up
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1 11.2 Start Thinking The circle in the diagram has a diameter of 14 inches. What is the area of the circle? Use the area of the circle to calculate the area of the sector created b the given measure of θ. C θ sector 1. θ = θ = θ = Warm Up Find the indicated measure. 1. area of a circle with a radius of 9 inches 2. area of a circle with a diameter of 4 feet 3. radius of a circle with an area of 100 square miles 4. diameter of a circle with an area of 42 square meters 5. area of a circle with a circumference of 12π centimeters 11.2 Cumulative Review Warm Up Find the values of and without using a calculator. Write our answers in simplest form Copright Big Ideas earning, C 379
2 Name Date 11.2 Puzzle Time What Driver Goes Around In Circles? Write the letter of each answer in the bo containing the eercise number. Complete the sentence. 1. A(n) of a circle is the region bounded b two radii of the circle and their intercepted arc. 2. The densit of a cit, count, or state is a measure of how man people live within a given area. Find the indicated measurement. Round our answer to the nearest hundredth. 3. area of a circle with radius 3 inches 4. area of a circle with diameter 12 feet 5. radius of a circle with area 42 square feet 6. radius of a circle with area 425 square inches 7. diameter of a circle with area 24.8 square inches 8. diameter of a circle with area 284π square centimeters 9. About 180,000 people live in a region with a 10-mile radius. Find the population densit in people per square mile. Round our answer to the nearest hundredth. Find the area of the indicated sector using the diagram. Round our answer to the nearest hundredth, if necessar. 10. m Z = 48, ZY = 6; Find the area in square units of the sector XZY. 11. area of sector XYZ = 50, m Z = 60 ; Find the area in square units of Z. 12. m Z = 55, ZY = 7; Find the area in square units of the sector XWY. W Z Answers. 320 C H R X W. sector S R. population T. section D A D high A E R. triangle R V C E S T I. 300 W X Y Copright Big Ideas earning, C 383
3 Name Date 11.2 Practice A In Eercises 1 4, find the indicated measure. 1. area of a circle with a radius of 6.8 feet 2. area of a circle with a diameter of 19.2 centimeters 3. radius of a circle with an area of square meters 4. diameter of a circle with an area of 707 square inches 5. About 1.2 million people live in a region with a 6-mile radius. Find the population densit in people per square mile. 6. A region with a 15-mile diameter has a population densit of about 5000 people per square mile. Find the number of people who live in the region. In Eercises 7 10, find the areas of the sectors formed b in ft Find the area of. 11. Find the area of H. F A = d2 1m 8 cm 70 E H 40 A = m2 G In Eercises 13 15, find the area of the shaded region ft ft 10 cm mm 10 cm 17 mm 16. The diagram shows the coverage of a securit camera outside a building. A new securit camera is installed in the same position that doubles the radius of the coverage area. How does this affect the coverage area? Eplain ft Copright Big Ideas earning, C
4 Name Date 11.2 Practice B In Eercises 1 4, 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 4. diameter of a circle with an area of square ards 5. About 150,000 people live in a circular region with a population densit of about 1578 people per square mile. Find the radius of the region. 6. About 1.75 million people live in a circular region with a population densit of about 5050 people per square mile. Find the radius of the region. In Eercises 7 10, find the areas of the sectors formed b cm in m d Find the radius of H. 12. Find the radius of. A = 4.8 cm 2 F E 88 H G 25 A = 1.05 ft 2 In Eercises 13 15, find the area of the shaded region m ft 6 in. 4 in. 16. A piece of cake is a sector of a clinder as shown. What is the volume of the piece of cake? 30 4 in. 5 in. Copright Big Ideas earning, C 381
5 Name Date 11.2 Enrichment and Etension Areas of Circles and Sectors 1. A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? 2. If the area of a sector is one-tenth of the area of the circle, what is the central angle of the sector? 3. In the diagram, the larger of the two concentric circles has a radius of 5 meters, and the smaller circle has a radius of 2 meters. What is the area of the shaded region in terms of π? Circle O is inscribed in equilateral triangle ABC and tangent to the sides of the triangle. If the area of ABC is 24 3 square units, what is the area of circle O? 5. The central angles of a target measure 45. The inner circle has a radius of 1 foot, and the outer circle has a radius of 2 feet. Assuming that all arrows hit the target at random, find the following probabilities. a. hitting a gra region b. hitting a black region c. hitting a gra or black region 6. ABC is formed b joining the centers of three congruent tangent circles. If the radius of each circle is 6 centimeters, find the area of ABC. 7. Consider an arc of a circle with a radius of 3 inches. a. Cop and complete the table. eave our answers in terms of π. easure of arc, Area of sector, b. Write an equation that represents the relationship between and. 382 Copright Big Ideas earning, C
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