The volume of a cone, given radius and height , can be calculated using the formula

.

We are given that , but we are not given the value of . We are given slant height , and since the cone is a right cone, its radius, height, and slant height can be related using the Pythagorean relation

.

Substituting 10 for and 20 for , we can find :

Now substitute in the volume formula:

To the nearest whole, this is 1,814.

The volume of a cone is given by the formula 

We are given that . Thus, the volume of our cone is given by

.

We are given that the volume of our cone is .

Thus,

so

and

.

Thus, 

.

so the correct answer is .

The surface area of a sphere can be calculated using the formula

Solving for :

Set and divide both sides by :

Take the square root of both sides:

Set in the volume formula:

,

the correct response.

The surface area of a sphere, given its radius , is equal to

Substitute for and solve for :

Divide by :

Extract the square root:

Substitute for in the volume formula:

,

the correct response.

A square has area formula

The total area required for the chickens will be

since each chicken requires  of space and there are  chickens.

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

.

For each state, divide the population by the land area. We can round each figure to the nearest whole for simplicity's sake.

Alabama:

 persons per square mile.

Arkansas:

 persons per square mile.

Kentucky:

 persons per square mile.

Mississippi:

 persons per square mile.

Tennessee:

 persons per square mile.

Tennessee has the greatest population density among the five states. 

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.

The county is in the shape of a trapezoid with bases of length  and , and with height . Its area in square miles can be found by substituting in the formula for the area of a trapezoid:

 square miles

Divide the population by this area to obtain an estimate of the population density:

 persons per square mile.

Of the given choices, 100 persons per square mile comes closest.

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 .

On the horizontal axis of a histogram, you have labels representing ranges of values. For example, the label "140–159" represents the range of islands with populations between 140 and 159. 

The question asks for the percent of islands with populations under 140. The ranges that are smaller than 140 are the "120–139" range and the "100–119" range. Match the bars of each with the percents on the vertical (y) axis. The percents corresponding to these ranges are 35% and 30%, respectively.

Adding both of these percents yields the answer, 65%.