Question

The average U.S. farm occupies 435 acres. How many square miles is this? \((1\) acre \(=43,560 \mathrm{ft}^{2}, 1\) mile \(=5280 \mathrm{ft})\)

Short answer

The average U.S. farm occupies approximately 0.679 square miles.

Step-by-step solution

Convert Acres to Square Feet

First, convert the farm size from acres to square feet using the conversion factor 1 acre = 43,560 square feet. Multiply the size of the farm in acres by the conversion factor: 435 acres * 43,560 square feet/acre.

Calculate the Total Square Feet

Perform the multiplication to find the total square feet: 435 * 43,560 = 18,948,600 square feet.

Convert Square Feet to Square Miles

Now convert the total square feet to square miles using the conversion factor 1 mile = 5,280 feet. Since there are 5,280 feet in a mile, there are 5,280 * 5,280 square feet in a square mile. Calculate this area and then divide the total square feet of the farm by this amount to convert to square miles.

Calculate the Area in Square Miles

Divide the total square feet by the number of square feet in a square mile: 18,948,600 square feet / (5,280 feet/mile * 5,280 feet/mile).

Perform the Division

Carry out the division to find the final area in square miles: 18,948,600 / 27,878,400 = 0.679 square miles.

Key concepts

Acre to Square Feet Conversion

Understanding how to convert acres to square feet is a key skill in various applications, including agriculture, real estate, and surveying. As we saw in our exercise, the conversion factor is very straightforward: 1 acre is equivalent to 43,560 square feet.

To perform this conversion, you simply multiply the number of acres by the conversion factor. If you're dealing with larger or smaller units, remember that multiplying by the conversion factor will scale up or down respectively. For instance, to convert 435 acres to square feet:

• Multiply the number of acres (435) by the conversion factor (43,560).
• Perform the calculation: 435 acres * 43,560 square feet/acre = 18,948,600 square feet.

This process is not only crucial for converting areas but also serves as a fundamental aspect of dimensional analysis, ensuring that units are consistent and calculations are accurate.

Square Feet to Square Miles Conversion

Once we have the area in square feet, it's common to need to convert it to larger units, like square miles, especially when dealing with vast expanses of land. To convert square feet to square miles, we use the conversion factor based on the number of feet in a mile, which is 5,280 feet.

Since a square mile is a mile by a mile, we find the area one square mile covers by squaring the number of feet in a mile:

• Calculate the area covered by one square mile: 5,280 feet/mile * 5,280 feet/mile = 27,878,400 square feet.
• To convert square feet to square miles, divide the area in square feet by the area of one square mile.

Following our exercise example, to convert 18,948,600 square feet to square miles:

• Divide 18,948,600 square feet by 27,878,400 square feet.
• The result is approximately 0.679 square miles.

This process allows us to move between different scales of measurement for area, facilitating comparisons and calculations for larger geographical areas.

Area Calculations

Area calculations are fundamental in many fields, from construction and landscaping to geography and property assessment. An area is a measure of the extent of a two-dimensional surface within boundaries, and it's typically measured in square units, like square feet or square miles in the case of the exercise.

The method of calculating area can vary depending on the shape and dimensions given. For rectangles and squares, the area is found by multiplying the length by the width. However, for conversion purposes, we often use predefined conversion factors to change one unit of area to another.

For accurate area calculations, it's essential to:

• Use the correct formula based on the shape and dimensions provided.
• Ensure that all measurements are in the same units before multiplying.
• Use conversion factors when changing units to maintain the integrity of the measurement.

With the right approach, area calculations don't have to be complicated, and they provide valuable information for various applications.

Dimensional Analysis

Dimensional analysis is a powerful tool used in solving problems that involve measurements and conversions among units. This technique ensures that the final answer of a calculation has the desired units and that the math carried out is dimensionally consistent.

When performing dimensional analysis:

• Units are treated as algebraic quantities that can cancel each other out when they appear on both sides of a ratio.
• We multiply or divide the given number by conversion factors that relate the units, aiming to cancel out unwanted units.
• We check that the resulting units match the units required for the answer.

In our exercise, we used dimensional analysis to convert acres to square feet and then square feet to square miles, maintaining the consistency of units throughout the process, which ensures accurate and meaningful results when dealing with real-world problems.