Problem 6 - University Physics with Modern Physics

Question

A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft\(^2\). If a lot has an area of 12.0 acres, what is its area in hectares?

Step-by-Step Solution

Answer

The area of the lot is approximately 4.8613 hectares.

Step 1: Convert acres to square feet

We know that 1 acre is equivalent to 43,600 ft². To find the area of the lot in square feet, multiply the number of acres by the area per acre: \[\text{Area in ft}^2 = 12.0 \text{ acres} \times 43,600 \text{ ft}^2/\text{acre}\]\[\text{Area in ft}^2 = 523,200 \text{ ft}^2\]

Step 2: Convert square feet to square meters

There are 0.092903 square meters in a square foot. To convert from square feet to square meters, multiply the area by this conversion factor:\[\text{Area in m}^2 = 523,200 \text{ ft}^2 \times 0.092903 \text{ m}^2/\text{ft}^2\]\[\text{Area in m}^2 \approx 48,612.8236 \text{ m}^2\]

Step 3: Convert square meters to hectares

Since 1 hectare is defined as 10,000 square meters, convert square meters to hectares by dividing by 10,000:\[\text{Area in hectares} = \frac{48,612.8236 \text{ m}^2}{10,000 \text{ m}^2/\text{hectare}}\]\[\text{Area in hectares} \approx 4.8613 \text{ hectares}\]

Key Concepts

Area Conversion

Understanding area conversion is essential, especially in various fields like physics, real estate, and agriculture, where different units are used in different regions.

Converting area units allows us to communicate measurements accurately and effectively. For example, in America, you'll often hear area described in acres or square feet, whereas in Europe, square meters or hectares are more common.

Converting between these units involves knowing specific conversion factors. It’s a process that helps streamline calculations across different measurement systems, ensuring clarity and consistency in communications and problem-solving.

• Multiply measurements with conversion factors for direct conversion.
• Understand the context in which certain units are used.
• Keep track of units throughout calculations to avoid mistakes.

Square Feet to Square Meters

When converting square feet into square meters, you use a constant conversion factor.

Specifically, there are approximately 0.092903 square meters in one square foot.
This conversion is crucial when dealing with international contexts, like real estate, where properties might be measured in square feet but need to be evaluated in metric units. To perform the conversion, follow these steps:

• Take the number of square feet.
• Multiply by 0.092903 to get the area in square meters.

This straightforward multiplication gives you the square meters equivalent, allowing for seamless comparisons or calculations with other metric-based measurements.

Square Meters to Hectares

Converting square meters to hectares is a common problem, particularly in agriculture and large-scale land management.

One hectare is defined as 10,000 square meters. When you need to convert, you simply divide the number of square meters by 10,000.

• This means for every 10,000 square meters, you have one hectare.
• Using division ensures accuracy when scaling areas from smaller plots to expansive fields.

This conversion is vital for understanding and communicating the size of agricultural plots, especially those measured using the metric system. Having a quick way to switch between these units can provide better insights into planning and resource management.

Physics Problem-Solving

Physics problem-solving often involves several steps and the use of conversion factors, as seen in complex area conversion problems.

This methodical approach helps break down the problem into manageable parts, making it easier to tackle. You start by identifying the units you are given and the units you need. Incorporating conversion factors, you methodically convert from one unit to another.

• Always begin with a known conversion: be it a standard like 1 acre = 43,600 ft².
• Convert using set factors with care, ensuring numbers and units align.
• Finally, verify your results for realism and accuracy.

This approach illustrates how methodical problem-solving enables accurate and intentional outcomes, facilitating better understanding and application in physics and mathematics.