1. Modeling with Geometry
2018 Geometry Bootcamp
2018
Modeling with Geometry
2018 Geometry Bootcamp

2. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.1
The surface area of a baseball is 177cm2. What is the diameter of the baseball? (Use 3.14 for .)
3.75 cm
7 cm
7.5 cm
14.1 cm
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

3. 2018 Geometry Bootcamp
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.
Groups 1, 2, and 3
37.7
2018 Geometry Bootcamp

4. 2018 Geometry Bootcamp
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 ft2)
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.
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

5. 2018 Geometry Bootcamp
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?
The brick has a greater volume than the block and a smaller mass, so the brick is less dense than the block.
The block has a smaller volume than the brick and a greater mass, so the brick is more dense than the block.
The brick is half the volume of the block and more than half the mass, so the brick is more dense than the block.
The block is twice the volume of the brick and more than double the mass, so the brick is less dense than the block.
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

6. MAFS.912.G-MG.1.2 Enter your answer in the box. 0.002
2018 Geometry Bootcamp
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.
Groups 1, 2, and 3
0.002
2018 Geometry Bootcamp

7. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.2
Lead has a density of 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.
Groups 1, 2, and 3
1396
2018 Geometry Bootcamp

8. 2018 Geometry Bootcamp
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?
Groups 1, 2, and 3
Mexico City, Sao Paolo, Seoul, Tokyo
Sao Paolo, Tokyo, Seoul, Mexico City
Seoul, Sao Paolo, Mexico City, Tokyo
Tokyo, Mexico City, Sao Paolo, Seoul D
2018 Geometry Bootcamp

9. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.2
Britney found an irregularly shaped metal object on the beach that has a mass of 𝑔𝑟𝑎𝑚𝑠. To determine the volume, she partially filled a cylindrical water bottle and dropped the object in. The water level in the bottle rose by 1.2 𝑐𝑚. The bottle has a diameter of 5 𝑐𝑚. Calculate the density of the metal to determine what type of metal Britney found. Densities, measured in grams per cubic centimeters, 𝑔 𝑐𝑚 3 , for some common metals are listed.
Copper: 8.86 𝑔 𝑐𝑚 3
Bronze: 9.87 𝑔 𝑐𝑚 3
Silver: 10.5 𝑔 𝑐𝑚 3
Gold: 19.3 𝑔 𝑐𝑚 3
Groups 1, 2, and 3
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
2018 Geometry Bootcamp

10. 2018 Geometry Bootcamp
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
Groups 1, 2, and 3
2018 Geometry Bootcamp

11. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.2
A machinist creates a solid steel part for a wind turbine engine. The part has a volume of 1,015 cubic centimeters. Steel can be purchased for $0.29 per kilogram, and has a density of 7.95 𝑔/ 𝑐𝑚 3 .
If the machinist makes 500 of these parts, what is the cost of the steel, to the nearest dollar?
Enter your answer in the box.
1,170
Groups 1, 2, and 3
2018 Geometry Bootcamp

12. 2018 Geometry Bootcamp
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?
15.7 inches
31.4 inches
78.5 inches
99.3 inches
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

13. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.3
Roberto put new carpeting in one room of his house. The area of this room is represented in the scale drawing below. Scale: 1 𝑖𝑛𝑐ℎ=5.5 𝑓𝑒𝑒𝑡
If carpeting costs $5.40 per square foot, what is the total cost of the new carpeting for this room?
$256.50
$282.15
$1,282.50
$1,551.83
Groups 1, 2, and 3 D
2018 Geometry Bootcamp

14. 2018 Geometry Bootcamp
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
Groups 1, 2, and 3
2018 Geometry Bootcamp

15. 2018 Geometry Bootcamp
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
Groups 1, 2, and 3
2018 Geometry Bootcamp

16. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.3
A candle maker has cubic centimeters (cm3) 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? 6 7 25 26
Groups 1, 2, and 3 C
2018 Geometry Bootcamp

17. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.3
Sara builds floor lamps that fit into boxes that are 4 feet by 2 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? 4 5 6 7
Groups 1, 2, and 3 B
2018 Geometry Bootcamp

18. 2018 Geometry Bootcamp
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
Groups 1, 2, and 3
2018 Geometry Bootcamp

19. 2018 Geometry Bootcamp
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?
Groups 1, 2, and 3
Enter your answer in the box.
400
2018 Geometry Bootcamp

20. 2018 Geometry Bootcamp
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
A metal pole is used to measure how much gas is in the tank.
To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank?
[1 𝑓𝑡 3 =7.48 𝑔𝑎𝑙𝑙𝑜𝑛𝑠]
Groups 1, 2, and 3
2018 Geometry Bootcamp

21. 2018 Geometry Bootcamp
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
Groups 2 and 3
2018 Geometry Bootcamp

22. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.3
The figure shows the design of a greenhouse with a rectangular floor. The front and back sides of the greenhouse are semicircles with a diameter 𝑤, and the roof is half a cylinder. Consider greenhouse 𝐴 with floor dimensions 𝑤=16 feet and 𝑙=18 feet.
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
Part A
A concrete slab 4 inches deep will be poured for the floor of the greenhouse 𝐴. How many cubic feet of concrete are needed for the floor?
Groups 2 and 3
Enter your answer in the box.
Enter your answer in the box.
2,262 96
2018 Geometry Bootcamp

23. 2018 Geometry Bootcamp
MAFS.912.G-MG.1.3
The figure shows the design of a greenhouse with a rectangular floor. The front and back sides of the greenhouse are semicircles with a diameter 𝑤, and the roof is half a cylinder. Consider greenhouse 𝐴 with floor dimensions 𝑤=16 feet and 𝑙=18 feet.
Part D
For greenhouses of this type, which of the listed dimensions will the total cubic feet of space in the greenhouse be greeter than that of greenhouse 𝐴?
Part C
One air freshener can keep up to 1,500 cubic feet of air fresh. What is the minimum number of air fresheners needed to keep the air in greenhouse 𝐴?
𝑤=15 feet and 𝑙=19 feet
𝑤=15 feet and 𝑙=20 feet
𝑤=17 feet and 𝑙=16 feet
𝑤=18 feet and 𝑙=15 feet
𝑤=18 feet and 𝑙=16 feet
Groups 2 and 3
Enter your answer in the box. 2
2018 Geometry Bootcamp

24. 2018 Geometry Bootcamp
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 aquarium. She measures and finds that the water reaches to a height of 4 inches.
Then Moira puts the stones in the aquarium. She measures and finds that the water reaches to a new height of 7 inches.
Groups 2 and 3
Part A: Using this information, find the volume of the stones.
cubic inches
384
Continues on the next slide
2018 Geometry Bootcamp

25. 2018 Geometry Bootcamp
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.
Part C:
Which of the three shapes would be Moira’s best choice for a container for the stones? Explain.
cubic inches
cube
343
Groups 2 and 3
cubic inches
cylinder
628
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.
cubic inches
cone
340
2018 Geometry Bootcamp

26. 2018 Geometry Bootcamp
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.
The base of the shade will be a square measuring 18 feet by 18 feet. The height of the rectangular sides will be 9 feet. The measure of the angle made by the roof with the side of the shed can vary and is labeled as 𝑥°. Different roof angles create different surface areas of the roof. The surface area of the roof will determine the number of roofing shingles needed in constructing the shed. To meet drainage requirements, the roof angle must be at least 117°.
Groups 2 and 3
Part A: The builder of the shed is considering using an angle that measures 125°. Determine the surface area of the roof if the 125° angle is used.
square feet
395.5
Continues on the next slide
2018 Geometry Bootcamp

27. 2018 Geometry Bootcamp
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?
Part B: Without changing the measurements of the base of the shed, the builder is also considering using a roof angle that will create a roof surface area that is 10% less than the area obtained in Part A. Less surface area will require less roofing shingles. Will such an angle meet the specified drainage requirements? Explain.
A 10% decrease in the roof area obtained in Part A is about 356 𝑓𝑡 2 which means that one rectangle would have an area of about 178 𝑓𝑡 2 . If the base of the rectangle remains 18 feet, then the other side will be about 9.9 feet. With these measurements the angle will be 25°+90°=115°, and this would not meet the minimum requirement of 117°.
122.7
Groups 2 and 3
2018 Geometry Bootcamp