Problem 102 - Chemistry A Molecular Approach

Question

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre \(=43,560 \mathrm{ft}^{2}, 1 \mathrm{mi}=5280 \mathrm{ft}\) ). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?

Step-by-Step Solution

Answer

954 million acres of U.S. farmland is approximately 1491 square miles, which is about 42.13% of the total U.S. land area.

Step 1: Convert acres to square feet

Since 1 acre equals 43,560 square feet, multiply the total farmland acres by this conversion factor to find the area in square feet. \[ 954 \text{ million acres} \times 43,560 \text{ square feet/acre} = 41562464000 \text{ square feet} \]

Step 2: Convert square feet to square miles

Since 1 square mile is 5,280 feet by 5,280 feet, calculate the area of one square mile in square feet and then divide the total farmland square footage by this area to convert into square miles. \[ 1 \text{ mile}^2 = (5280 \text{ feet})^2 = 27878400 \text{ square feet} \ 41562464000 \text{ square feet} \div 27878400 \text{ square feet/mile}^2 = 1491 \text{ square miles} \]

Step 3: Calculate the percentage of U.S. land that is farmland

Divide the farmland area in square miles by the total U.S. land area in square miles and multiply by 100 to convert the fraction to a percentage. \[ \frac{1491 \text{ square miles}}{3.537 \text{ million square miles}} \times 100 \approx 42.13\% \]

Key Concepts

Acre to Square Feet Conversion

Understanding how to convert acres to square feet is crucial for many real-world applications, such as land management and agricultural planning. The conversion is straightforward: since one acre is defined as equal to 43,560 square feet, to make this conversion, you simply multiply the number of acres by 43,560.

For instance, if you have 954 million acres of farmland, as in our exercise, the calculation would be: \[ 954,000,000 \text{ acres} \times 43,560 \text{ square feet/acre} = 41,562,464,000 \text{ square feet} \]. This simple multiplication gives you the total square footage of an area measured in acres.

Square Feet to Square Miles Conversion

After converting acres to square feet, the next step often involves converting square feet to square miles. This can be vital for understanding the scale of larger areas, such as those used in geographic and urban planning.

A square mile is a square that is one mile on each side, and there are 5,280 feet in a mile. Therefore, one square mile is equivalent to \[ 5,280 \text{ feet} \times 5,280 \text{ feet} = 27,878,400 \text{ square feet} \].

To convert square feet to square miles, divide the number of square feet by 27,878,400. For our example with the farmland, the calculation is: \[ 41,562,464,000 \text{ square feet} \/ 27,878,400 \text{ square feet/mile}^2 = \text{approximately 1,491 square miles} \]. This provides a manageable figure to understand the scale of the area in question.

Percentage Calculation

Percentage calculations are a fundamental part of numeracy, helping to represent how one quantity relates to another as a fraction of 100. This is especially useful when comparing proportions, such as the part of the whole that is farmland in the United States.

In percentage calculations, you divide the part by the whole and then multiply by 100. Applying this to our exercise, to find out what percentage of the U.S. land area is farmland, you divide the farmland area in square miles by the total U.S. land area and multiply the result by 100: \[ \frac{1,491 \text{ square miles}}{3,537,000 \text{ square miles}} \times 100 = \text{approximately 42.13%} \].

This tells us that roughly 42.13% of the total U.S. land area is made up of farmland, a significant percentage that emphasizes the importance of agriculture in the country.