AnswersOC27 GEO-1206310-S2-Degele-VOL7006PDensity and Design Problems

Lesson 11.6: Density and Design Problems Answers

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The populations and areas of four states are shown.

Question illustration
A
The state with the lowest population has the greatest population density.
B
The state with the second lowest population has the lowest population density.
C
The state with the lowest population has the lowest population density.
D
The state with the second greatest population has the lowest population density.
2
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Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.

Question illustration
A
Design 1, because it requires 12 fewer feet of fencing than Design 2
B
Design 1, because it requires 24 fewer feet of fencing than Design 2
C
Design 2, because it requires 12 fewer feet of fencing than Design 1
D
Design 2, because it requires 24 fewer feet of fencing than Design 1
3

Marina wants to install security cameras in her store, which has dimensions 48 feet by 48 feet. Each camera can view an area of approximately 128 ft2, with a viewing area shaped like a right triangle. The distance between grid lines is 4 feet.

Question illustration
A
6
B
9
C
12
D
18
4

A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria.

Question illustration
A
Dish A has the lowest population density.
B
Dish C has the greatest population density.
C
Dish A and Dish B have approximately the same population density.
D
Dish C and Dish D have approximately the same population density.
5

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, a large farm harvested rice from 690 acres of farmland. The crop yield was 7,553 bushels per acre.Approximately how many bushels of rice were harvested?

A
0.1 million bushels
B
5.2 million bushels
C
8.2 million bushels
D
10.9 million bushels
6

High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in four different regions.

Question illustration
A
Region A
B
Region B
C
Region C
D
Region D
7

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75.Which packaging should the company use to minimize cost? Explain.

A
The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.
B
The cylindrical containers should be used because they will cost the company $2.50 less than using the rectangular boxes.
C
The rectangular prism boxes should be used because they will cost the company $5.00 less than using the cylindrical containers.
D
The cylindrical containers should be used because they will cost the company $5.00 less than using the rectangular boxes.
8

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 94,010 bushels of grain, resulting in a crop yield of 170 bushels per acre.To the nearest whole acre, how many acres were harvested?

A
453 acres
B
489 acres
C
509 acres
D
553 acres
9

A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindrical container can hold 126 beads. The wooden container costs the company $0.70, while the plastic container costs $0.40.Which container should the company use to minimize cost? Explain.

A
The wooden containers should be used because it will cost $5.40 more to use the plastic containers.
B
The plastic containers should be used because it will cost $5.40 more to use the wooden containers.
C
The wooden containers should be used because it will cost $16.20 more to use the plastic containers.
D
The plastic containers should be used because it will cost $16.20 more to use the wooden containers.
10

Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is foot by foot and costs $0.45 per tile. The rectangular tile is 2 feet by foot and costs $0.80 per tile.Which tile should Orchid choose to minimize costs? Explain.

Question illustration
A
She should choose the square tiles because the total cost will be $8 less.
B
She should choose the rectangular tiles because the total cost will be $8 less.
C
She should choose the square tiles because the total cost will be $14 less.
D
She should choose the rectangular tiles because the total cost will be $14 less.
11

A medical researcher has two petri dishes containing viruses. Dish B has a population density of 1.2 viruses per square millimeter. Dish A has an area of about 2,826 square millimeters.If both petri dishes have the same population density, approximately how many viruses are in Dish A?

A
2,355 viruses
B
3,391 viruses
C
23,550 viruses
D
33,912 viruses
12

A city’s bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized.The population of City A, in Texas, is 29,455 and covers an area of 19.42 mi2. The population of City B, in Alabama, is 34,890 and covers an area of 25.4 mi2.Which city’s residents are more likely to use public buses? Explain.

A
The residents of City B are more likely to use public transportation because the city has the lowest population density.
B
The residents of City B are more likely to use public transportation because the city has the highest population density.
C
The residents of City A are more likely to use public transportation because the city has the lowest population density.
D
The residents of City A are more likely to use public transportation because the city has the highest population density.
13

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 9,396 bushels of soybeans, resulting in a crop yield of 40.5 bushels per acre.To the nearest whole acre, how many acres were harvested?

A
232 acres
B
252 acres
C
285 acres
D
295 acres
14

The table shows the number of resident geese living in four different ponds.

Question illustration
A
Pond A
B
Pond B
C
Pond C
D
Pond D
15

Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.

Question illustration
A
Design 1, because it requires 12 fewer feet of fencing than Design 2
B
Design 1, because it requires 24 fewer feet of fencing than Design 2
C
Design 2, because it requires 12 fewer feet of fencing than Design 1
D
Design 2, because it requires 24 fewer feet of fencing than Design 1
16

A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria.

Question illustration
A
Dish A has the lowest population density.
B
Dish C has the greatest population density.
C
Dish A and Dish B have approximately the same population density.
D
Dish C and Dish D have approximately the same population density.
17

The populations and areas of four states are shown.

Question illustration
A
The state with the lowest population has the greatest population density.
B
The state with the second lowest population has the lowest population density.
C
The state with the lowest population has the lowest population density.
D
The state with the second greatest population has the lowest population density.
18

A shoe store owner is designing the layout of the displays in his store. The floor area for the store is 1,600 square feet. The owner wants to have circular displays for the shoes, each with a radius of 6 feet, and a 48-square-foot rectangular cashier’s station in the corner. Customers should be able to easily walk around the shoe displays, so there must be at least a 4-foot walkway around each. The owner started drawing the layout shown.The distance between grid lines is 4 feet.

Question illustration
A
Three circular displays can be placed in one row, exactly as shown on the given grid.
B
Two circular displays can be placed so they are each the same distance from the cashier’s station.
C
The maximum number of circular displays that can be used is 4.
D
The maximum number of circular displays that can be used is 5.
19

Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is foot by foot and costs $0.45 per tile. The rectangular tile is 2 feet by foot and costs $0.80 per tile.Which tile should Orchid choose to minimize costs? Explain.

Question illustration
A
She should choose the square tiles because the total cost will be $8 less.
B
She should choose the rectangular tiles because the total cost will be $8 less.
C
She should choose the square tiles because the total cost will be $14 less.
D
She should choose the rectangular tiles because the total cost will be $14 less.
20

The population density of Peru one year was approximately 23 people per square kilometer. Brazil has a land area of approximately 8.5 million square kilometers.If Brazil had the same population density as Peru that year, approximately how many people were living in Brazil?

A
370,000 people
B
2,700,000 people
C
31,500,000 people
D
195,500,000 people

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