6.11.4 Test (TS): Circles Without Coordinates Test Geometry Sem 1 (S3537251) Julio Duenas Points possible: 50 Date: ____________ Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work. 1. A central angle is an angle whose vertex is at the center of a circle. Find the . Part I: Given that bisects use the diagram above to complete the following statement. (1 point) Part II: Find the . Explain your answer. (2 points) Part III: Find the . Show your work. (1 point) 2. An arc is a smooth piece of a circle. A major arc of a circle is an arc that is longer than half the circumference of the circle. Find the measure of the major arc . Part I: The is equal to/one half of the . (Circle one) (1 point) Part II: Using the relationship you established in Part I, find the . Show your work and explain your answer. (2 points) Part III: Using your answer from Part II, find the . Show your work. (2 points) 3. Find the measure of , , and . Part I: An inscribed angle is an angle formed by two chords of a circle which share an endpoint. Find the measure of inscribed angle . 1. Determine the relationship between the and the by circling one of the statements below. (1 point) a. b. c. b. Use the relationship you established in part 1 to find the . Show your work. (1 point) Part II: A secant is a line or segment that passes through a circle in two places. In the diagram above, find the , which is formed by two secants. 1. Determine the method of finding the by circling one of the statements below. (1 point) a. = b. = c. = d. = 2. Use the relationship you established in part 1 to find the . Show your work. (2 points) Part III: Use the method from Part I to find the . (1 point) 4. Find the difference between the area of a circular table with diameter 8 feet and a circular table with diameter 10 feet. Round your answer to the nearest hundredth. Show your work. Part I: Which of the following is the formula for finding the area of a circle? (Circle one) (1 point) a. b. c. d. Part II: Use the formula you selected in Part I to find the area of a circle with diameter 8 feet. Show your work and round your answer to the nearest hundredth. (2 points) Part III: Use the formula you selected in Part I to find the area of a circle with diameter 10 feet. Show your work and round your answer to the nearest hundredth. (2 points) Part IV: Find the difference of your answers from Part II and Part III to find the difference in the areas. Show your work and round your answer to the nearest hundredth. (1 point) Part V: The 8 foot diameter circular table has a 4 foot wide extension. What is the total area with the extension? How does the area compare to the area of the 10 foot diameter table? Show your work. (3 points) 5. A circle has center C, as shown below, and diameter 32 cm. Find the length of if . Part I: What fractional part of the circle's circumference is ? (Hint: A circle has .) (1 point) Part II: Use the fraction you determined in Part I and the circumference formula to find the length of . Show your work and round your answer to the nearest hundredth. (2 points) 6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboard that has a diameter of 20 in and it is divided into 20 congruent sectors. Find the area of one sector. Part I: Find the central angle. (Hint: A circle has .) (1 point) Part II: Use your answer from Part I to find the fraction of the circle that one sector will take up. (1 point) Part III: Use the fractional part from Part II with the area formula to find the area of one sector of the circle to the nearest tenth. (2 points) 7. Kendall bought 3 glazed donuts and 3 filled donuts and they fit perfectly in the 9" by 6" box. What is the area of the bottom of the box (the shaded region) not covered by donuts? Part I: What is the area covered by the three filled donuts? Round your answer to the nearest hundredth. Show your work and explain your reasoning. (4 points) Part II: What is the area covered by the three glazed donuts? Round your answer to the nearest hundredth. Show your work and explain your reasoning. (3 points) Part III: What is the area of the bottom of the box not covered by donuts? Show your work and explain your reasoning. (2 points) 8. The school track has eight lanes. Each lane is 1.25 meters wide. The arc at each end of the track is 180. The distance of the home straight and the radii for the arcs in the first four lanes are given. Part I: Find the radii of lanes 5 through 8 of the track. Show your work. (2 points) Part II: If Max ran around lane 1, how far did he run? Show your work and explain your solution. Round your answer to the hundredths. (3 points) Part III: Max wants to run a total of 3 laps around the track. Choose two additional lanes (2-8) for him to run and find the distance around those two lanes. Show your work and round your answer to the hundredths. (4 points) Part IV: Based on your lane choices in Part III, what was the total distance Max ran in the three laps around the track? Show your work. (1 point) Copyright 2016 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use . Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning and the Apex Learning Logo are registered trademarks of Apex Learning Inc