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 ft2. If a lot has an area of 12.0 acres, what is its area in hectares?

Ch 01: Units, Physical Quantities & Vectors

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 01: Units, Physical Quantities & Vectors

Problem 6

Chapter 1, Problem 6

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 ft². If a lot has an area of 12.0 acres, what is its area in hectares?

Verified step by step guidance

First, understand the conversion between acres and square feet. 1 acre is equivalent to 43,600 square feet.

Next, convert the area of the lot from acres to square feet. Multiply the area in acres (12.0 acres) by the conversion factor (43,600 ft²/acre) to find the area in square feet.

Now, convert the area from square feet to square meters. Use the conversion factor: 1 square foot is equal to 0.092903 square meters.

Once you have the area in square meters, convert it to hectares. Remember that 1 hectare is equal to 10,000 square meters.

Finally, express the area of the lot in hectares, using the conversion from square meters to hectares.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another. In this problem, converting acres to hectares is essential. Knowing the conversion factors between different units of area, such as square meters, square feet, acres, and hectares, allows for accurate calculations and comparisons between different measurement systems.

Area Calculation

Area calculation involves determining the size of a surface or a two-dimensional space. The problem requires understanding the area of a square field and comparing it to other units of area. Recognizing that 1 hectare equals 10,000 square meters and 1 acre equals 43,560 square feet is crucial for converting between these units and solving the problem.

Dimensional Analysis

Dimensional analysis is a method used to convert one kind of unit to another using conversion factors. It involves multiplying the given quantity by conversion factors that cancel out the original units and introduce the desired units. This technique is vital for ensuring that calculations are consistent and accurate, especially when dealing with complex unit conversions like acres to hectares.

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