Density and Design Problems Answers

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

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 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 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.

The populations and areas of four states are shown.

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.

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.

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.

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.