Density and Design Problems — Unit test Answers

The populations and areas of four states are shown.

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.

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.

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

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?

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.

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.

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 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.

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.