Density and Design Problems

Question 1

Tyler and Bethany have 240 feet of fencing with which to build a garden. Tyler wants the garden to be in the shape of a square, while Bethany wants it to be rectangular with a length of 50 feet and a width of 70 feet. Which design would give the maximum area for the garden? Explain.

Revolt · Accepted Answer

Tyler’s design would give the larger garden because the area would be 3,600 ft2.

Question 2

112.5225337.5✔ 450

Revolt · Accepted Answer

✔ 450

Question 3

✔ the rectangular containers, because it will cost the company $67 more to use the cylindrical containersthe cylindrical containers, because it will cost the company $67 more to use the rectangular containersthe rectangular containers, because it will cost the company $48 more to use the cylindrical containersthe cylindrical containers, because it will cost the company $48 more to use the rectangular containers

Revolt · Accepted Answer

✔ the rectangular containers, because it will cost the company $67 more to use the cylindrical containers

Question 4

Which statements are true? Check all that apply.

Revolt · Accepted Answer

The population density for Montana can be found using the ratio 1,005,141:145,552.; The state with the smallest population density is Montana.

Question 5

246✔ 8

Revolt · Accepted Answer

✔ 8

Question 6

The population density of New Jersey is about 1,195 people per square mile. Texas has a land area of 261,797 square miles. If Texas had the same population density as New Jersey, how many people would be living in that state?

Revolt · Accepted Answer

312,847,415

Question 7

The irrigation design for a new backyard is shown with six sprinkler heads and two walkways. Which statement is true of this design?

Revolt · Accepted Answer

The area covered by all the sprinkler heads together is approximately 169.64 ft2.

Question 8

A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.

Revolt · Accepted Answer

143; 157; the rectangular containers, because it will cost the company $67 more to use the cylindrical containers

Question 9

A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.

Revolt · Accepted Answer

✔ 143; 143; 157; the rectangular containers, because it will cost the company $67 more to use the cylindrical containers

Question 10

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 Belmont, MA, is 24,729 and covers an area of 4.66 mi2. The population of Easton, MA, is 23,112 and covers an area of 28.4 mi2. Which city’s residents are more likely to use public buses? Explain.

Revolt · Accepted Answer

The residents of Belmont are more likely to use public transportation because the city has the highest population density.

Density and Design Problems Answers

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