Density and Design Problems — Quiz Answers

A company needs to package 7 comma 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 point 7 0 dollars , while the plastic container costs 0 point 4 0 dollars Which container should the company use to minimize cost? Explain.

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 comma 396 bushels of soybeans, resulting in a crop yield of 40 point 5 bushels per acre. To the nearest whole acre, how many acres were harvested?

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 comma 455 and covers an area of 19 point 4 2 mi squared The population of City B, in Alabama, is 34 comma 890 and covers an area of 25 point 4 mi squared Which city’s residents are more likely to use public buses? Explain.

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 company needs to package 2 comma 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 point 5 0 dollars , while each cylindrical container costs 0 point 7 5 dollars Which packaging should the company use to minimize cost? Explain.

The population density of Peru one year was approximately 23 people per square kilometer. Brazil has a land area of approximately 8 point 5 million square kilometers. If Brazil had the same population density as Peru that year, approximately how many people were living in Brazil?

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 comma 533 bushels per acre. Approximately how many bushels of rice were harvested?

A medical researcher has two petri dishes containing viruses. Dish B has a population density of 1 point 2 viruses per square millimeter. Dish A has an area of about 2 comma 826 square millimeters. If both petri dishes have the same population density, approximately how many viruses are in Dish A?

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 1 half foot by 1 half foot and costs 0 point 4 5 dollars per tile. The rectangular tile is 2 feet by 1 fourth foot and costs 0 point 8 0 dollars per tile. Which tile should Orchid choose to minimize costs? Explain.

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?