2019 GEOMETR Y boot camp Modeling with Geometry

MAFS. 912. G-MG. 1. 1 The surface area of a baseball is 177 cm 2. What is the diameter of the baseball? (Use 3. 14 for. ) A. 3. 75 cm B. 7 cm C. 7. 5 cm D. 14. 1 cm C

MAFS. 912. G-MG. 1. 1 The waffle cones at the ice cream shop have a radius of 2 inches and a height of 6 inches. They are made using a triangular piece of waffle material, as shown. What is the approximate area, in square inches, of the triangular piece of waffle material used for the waffle cone? Round your answer to the nearest tenth. Enter your answer in the box. 37. 7

MAFS. 912. G-MG. 1. 1 A farmer wants to buy between 90 and 100 acres of land. • He is interested in a rectangular piece of land that is 1, 500 yards long and 300 yards wide. • The piece of land is being sold as one complete unit for $87, 000. If the farmer does not want to spend more than $900 an acre, does the land meet all of his requirements? (1 acre ≈ 43, 560 ft 2) A. B. C. D. Yes, the amount of land satisfies his needs, and the price is low enough. No, the price is low enough, but there is too much land. No, the price is low enough, but there is not enough land. No, the amount of land satisfies what he needs, but the price is too high. D

NEW! MAFS. 912. G-MG. 1. 1 A vendor is using an 8 -ft by 8 -ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft. What is the volume, in cubic feet, of space the tent occupies? A. 256 B. 640 C. 672 D. 768 B

NEW! MAFS. 912. G-MG. 1. 1 The Fun Run organizers want to provide cylindrical cups of water to all runners after the race. The cups have a base diameter of 2. 5 inches and a height of 5 inches. How much water should the organizers estimate to serve each runner? (Assume each runner will only drink one cup of water. ) A

NEW! MAFS. 912. G-MG. 1. 1 Francisco needs the three pieces of glass shown below to complete a stainedglass window. The shapes, two triangles and a trapezoid, are measured in inches. Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window? A. 20 B. 25 C. 29 D. 34 A

NEW! MAFS. 912. G-MG. 1. 1 A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path. 3371

NEW! MAFS. 912. G-MG. 1. 1 203

NEW! MAFS. 912. G-MG. 1. 1 Ian needs to replace two concrete sections in his sidewalk, as modeled below. Each section is 36 inches by 36 inches and 4 inches deep. He can mix his own concrete for $3. 25 per cubic foot. How much money will it cost Ian to replace the two concrete sections? 19. 50

MAFS. 912. G-MG. 1. 2 Veronica’s science class is studying density, and each student is asked to bring in an object to determine its density. Veronica brings in a brick that weighs two pounds and is 6 inches long, 3 inches wide, and 2 inches tall. Her friend Becky brings in a block of wood that weighs 3 pounds and is 1 foot long, 2 inches wide, and 3 inches tall. Which is a true statement about the objects? A. The brick has a greater volume than the block and a smaller mass, so the brick is less dense than the block. B. The block has a smaller volume than the brick and a greater mass, so the brick is more dense than the block. C. The brick is half the volume of the block and more than half the mass, so the brick is more dense than the block. D. The block is twice the volume of the brick and more than double the mass, so the brick is less dense than the block. C

MAFS. 912. G-MG. 1. 2 The table shows the square footage of various high schools in a city and the number of students who attend that school. What is the population density of the school that has the lowest number of students per square foot? Give your answer to three decimal places. Enter your answer in the box. 0. 002

MAFS. 912. G-MG. 1. 2 Lead has a density of 11. 36 grams per cubic centimeter. Iron has a density of 7. 87 grams per cubic centimeter. A rectangular prism with dimensions 5 centimeters by 10 centimeters by 8 centimeters is made of each material. To the nearest gram, how much greater is the mass of the prism made of lead than the one made of iron? Enter your answer in the box. 1396

MAFS. 912. G-MG. 1. 2 The following table provides a list of four international cities, their populations, and the area of the cities. Determine the population densities of each city and then order them from least to greatest. Which list shows the population densities of each city in order from least to greatest? A. B. C. D. Mexico City, Sao Paolo, Seoul, Tokyo Sao Paolo, Tokyo, Seoul, Mexico City Seoul, Sao Paolo, Mexico City, Tokyo, Mexico City, Sao Paolo, Seoul D

MAFS. 912. G-MG. 1. 2 Select the word that correctly completes the sentence. Based on the density of the metal, it is most likely that the metal Britney found is

MAFS. 912. G-MG. 1. 2 Hanna has a cone made of steel and a cone made of granite. • Each cone has a height of 10 centimeters and a radius of 4 centimeters. • The density of steel is approximately 7. 75 grams per cubic centimeter. • The density of granite is approximately 2. 75 grams per cubic centimeter. What is the difference, to the nearest gram, of the masses of the cones? 838

MAFS. 912. G-MG. 1. 2 Enter your answer in the box. 1, 170

NEW! MAFS. 912. G-MG. 1. 2

NEW! MAFS. 912. G-MG. 1. 2 Shae has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The total weight of the bag, pole, and unfilled base is 270 pounds. The cylindrical base is 18 inches tall with a diameter of 20 inches. The dry sand used to fill the base weighs 95. 46 lbs. per cubic foot. To the nearest pound, determine and state the total weight of the training equipment if the base is filled to 85% of its capacity. Enter your answer in the box. 536

MAFS. 912. G-MG. 1. 3 A cube-shaped packing box like the one shown below is used to pack a stack of dinner plates. If the volume of the box is 1, 000 cubic inches, what is the maximum circumference of the dinner plates that will fit in the box, to the nearest tenth of an inch? A. 15. 7 inches B. 31. 4 inches C. 78. 5 inches D. 99. 3 inches B

MAFS. 912. G-MG. 1. 3 If carpeting costs $5. 40 per square foot, what is the total cost of the new carpeting for this room? A. $256. 50 B. $282. 15 C. $1, 282. 50 D. $1, 551. 83 D

MAFS. 912. G-MG. 1. 3 Kevin designed the container below to hold a solid cylindrical tube with gel to surround and insulate the tube. The container is a rectangular prism, and the tube has a diameter of 0. 75 inch and a length of 3. 5 inches, as shown. Calculate the volume, in square inches, of gel the container will hold when the tube is in the container. 3. 92

MAFS. 912. G-MG. 1. 3 Jackson has a table with a square top and he wants to buy a circular piece of lace that will cover the entire top of the table. The table has side lengths of 12 inches, as shown. What is the area, in square inches, of the smallest circular piece of lace Jackson could by? Round your answer to the nearest tenth. 226. 2

MAFS. 912. G-MG. 1. 3 A candle maker has 301. 59 cubic centimeters (cm 3) of liquid wax to make cone-shaped candles. Each candle has a circular base with a diameter of 3 cm and a height of 5 cm. What is the maximum number of candles that can be made from the liquid wax? A. 6 B. 7 C. 25 D. 26 C

MAFS. 912. G-MG. 1. 3 Sara builds floor lamps that fit into boxes that are 4 feet by 2 feet. The bed of her pickup truck has a maximum clearance that is 54 inches wide by 10 feet long and a hard cover that lies flat at 30 inches from the bottom. How many boxes of lamps can Sara fit into her truck at one time? A. 4 B. 5 C. 6 D. 7 B

MAFS. 912. G-MG. 1. 3 Miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog can run freely. What is the maximum area, in square feet, he can enclose? Enter your answer in the box. 625

MAFS. 912. G-MG. 1. 3 In order to find the density of a rock, Michael needs to find the volume of the rock. Michael has a container in the shape of a rectangular prism. The base of the container is 20 centimeters long and 10 centimeters wide. The height of the container is 12 centimeters. Michael puts water in the prism until the height of the water is 6 centimeters. He then puts the rock in the water so that it is completely submerged. The water rises to a height of 8 centimeters. What is the volume, in cubic centimeters, of the rock? Enter your answer in the box. 400

MAFS. 912. G-MG. 1. 3 A gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum of 20, 000 gallons of gasoline and has a length of 34. 5 feet. 10. 9

MAFS. 912. G-MG. 1. 3 An organic foods company needs to paint its new silo. The silo is a cylinder with a height of 24 yards and a base 3 yards in diameter, as shown below. The paint the company has selected will cover 150 square feet per gallon. How many gallons of paint will be needed to paint the roof and the walls of the silo? Enter your answer in the box. 14

MAFS. 912. G-MG. 1. 3 Part B The cylindrical roof of greenhouse A will be constructed from aluminum. The aluminum cost $5. 00 per square foot. What will be the cost of the minimum amount of aluminum needed to construct the roof? Give your answer to the nearest dollar Enter your answer in the box. 96 Enter your answer in the box. 2, 262

MAFS. 912. G-MG. 1. 3 Enter your answer in the box. 2

MAFS. 912. G-MG. 1. 3 Moira collected some stones at the beach. Now she wants to make a clear plastic container to display the stones. To plan the container, Moira decides that she must first find the volume of the stones. Moira has an aquarium that is shaped like a rectangular prism. It is 8 inches wide, 16 inches long, and 10 inches high. She plans to use the aquarium to find the volume of the stones. First, Moira pours some water into the Then Moira puts the stones in the aquarium. She measures and finds that the water reaches to a height of 4 inches. reaches to a new height of 7 inches. Part A: Using this information, find the volume of the stones. 384 cubic inches Continues on the next slide

MAFS. 912. G-MG. 1. 3 Part B: Moira is considering three possible shapes for the container that will hold the stones. The shapes are shown below. Moira is considering three possible Find the volume of each shape to the nearest whole number. cube 343 cubic inches cylinder 628 cubic inches cone 340 cubic inches Part C: Which of the three shapes would be Moira’s best choice for a container for the stones? Explain. The cylinder. The stones have irregular shapes, so there will be some empty space between them when they are placed in the container. This means that the volume of the container must be a bit greater than 384 cubic inches.

MAFS. 912. G-MG. 1. 3 The figure shows the design of a shed that will be built. Use the figure to answer all parts of the task. 395. 5 square feet Continues on the next slide

MAFS. 912. G-MG. 1. 3 Part C: The roofing shingles cost $27. 75 for a bundle. Each bundle can cover approximately 35 square feet. Shingles must be purchased in full bundles. The builder has a budget of $325 for shingles. What is the greatest angle, to the nearest tenth, the builder can use and stay within budget? 122. 7

NEW! MAFS. 912. G-MG. 1. 3 An architect is designing a building topped with a hemispherical dome. She creates a scale model of the building using a scale of 0. 25 inch : 1 foot. In the scale model, the diameter of the dome is 23. 75 inches. What will be the circumference, in feet, of the actual dome? Note: 298. 45 is also considered a correct answer

NEW! MAFS. 912. G-MG. 1. 3 David plans to cover the floor of his room with new material. • The floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length. • Each piece of new material has an area of 2. 5 square feet. Assuming the pieces of new material can be cut as needed, how many pieces does David need? A. 101 B. 126 C. 202 D. 252 A

Acknowledgment The assessment items presented in this Power. Point have been compiled from several free web-based resources like sample items, released items, and practice tests. • Regent Exams - http: //www. jmap. org/JMAP_REGENTS_EXAMS. htm • PARCC Released Items - https: //parcc-assessment. org/released-items/ • NCFE Released Items For High School Subjects (2017 -18) - http: //www. ncpublicschools. org/accountability/testing/common-exams/releaseditems/highschoolitems • Ohio Student Practice Resources – Mathematics - https: //oh. portal. airast. org/resources/mathematics-spr/