HiSET: Math : Apply concepts of density in modeling situations
Study concepts, example questions & explanations for HiSET: Math
All HiSET: Math Resources
Example Questions
Example Question #1 : Apply Concepts Of Density In Modeling Situations
A farmer has to make a square pen to hold chickens. If each chicken has to have 
A square has area formula
The total area required for the chickens will be
since each chicken requires 
Thus, we have
for the length of our chicken fence.
Since there are four sides of a square and each side has a length of 5, the total length of fence required is
Example Question #1 : Apply Concepts Of Density In Modeling Situations
Source: United States Census Bureau
The average population density of a geographic area is defined to be the average number of residents per square mile.
Above is a table with the land areas and populations of five states.Which state among the five has the greatest population density?
Kentucky
Mississippi
Arkansas
Tennessee
Alabama
Tennessee
For each state, divide the population by the land area. We can round each figure to the nearest whole for simplicity's sake.
Alabama:
Arkansas:
Kentucky:
Mississippi:
Tennessee:
Tennessee has the greatest population density among the five states.
Example Question #3 : Apply Concepts Of Density In Modeling Situations
Source: United States Census Bureau
The average population density of a geographic area is defined to be the average number of residents per square mile.
Above is a table with the population densities and the land areas of five states. Of the five, which state has the greatest population?
South Dakota
North Dakota
Vermont
Wyoming
Alaska
South Dakota
Multiply the population density of each state by its corresponding area to get an estimate of the population (round to the nearest thousand for simplicity's sake):
Alaska:
North Dakota:
South Dakota:
Vermont:
Wyoming:
Of the five states, South Dakota is the most populous.
Example Question #1 : Apply Concepts Of Density In Modeling Situations
The average population density of a geographic area is defined to be the average number of residents per square mile.
Above is the map of a county whose population is about 120,000. Which of the following is the best estimate of the average population density?
150 persons per square mile
50 persons per square mile
100 persons per square mile
200 persons per square mile
250 persons per square mile
100 persons per square mile
The county is in the shape of a trapezoid with bases of length 
Divide the population by this area to obtain an estimate of the population density:
Of the given choices, 100 persons per square mile comes closest.
Example Question #1 : Apply Concepts Of Density In Modeling Situations
The graphic below shows a blueprint for a swimming pool.
If the pool is going to be 66 inches deep, how many cubic feet of water will it be able to hold? (1 ft = 12 in)
Notice that the outer dimensions of the blueprint are the dimensions for the entire pool, including the concrete, while the inner dimensions are for the part of the pool that will be filled with water. Therefore, we want to focus on just the inner dimensions.
Notice that the depth is given in inches, while the dimensions are in feet. Convert 66 inches to feet by dividing 66 by 12, since 12 inches makes a foot:
The inch units cancel out and leave us with just the feet units. 66 in is 5.5 ft.
Now we have all of the information we need to solve for the volume of the pool. The pool is a rectangular prism, and the formula for volume of a rectangular prism is
(In this case, the "height" of the swimming pool is its depth.)
The blueprint shows that the pool is 40 ft long and 30 ft wide. Plugging in the measurements from the problem, we get
Multiplying this out, we get 
Certified Tutor
Certified Tutor
All HiSET: Math Resources
