Calculating Population In A Circular Region Radius 13.9 Km And Density 560 People Per Sq Km

Understanding population density is crucial in various fields, from urban planning to environmental science. It helps us analyze how people are distributed across a given area and provides insights into resource allocation, infrastructure development, and potential environmental impacts. In this comprehensive guide, we will delve into the process of calculating the population within a circular region, using a practical example to illustrate the steps involved. Our specific scenario involves a circular region with a radius of 13.9 kilometers and a population density of 560 people per square kilometer. We aim to determine the total number of people living in this region, rounding our final answer to the nearest person. This exercise will not only enhance your understanding of population density calculations but also demonstrate the application of geometric principles in real-world scenarios. Whether you are a student, researcher, or simply someone curious about population dynamics, this guide will provide you with the knowledge and tools to tackle similar problems effectively. By the end of this article, you will be able to confidently calculate population sizes in circular regions and appreciate the significance of these calculations in various contexts.

Understanding Population Density

Before we dive into the calculations, let's clarify the concept of population density. Population density is defined as the number of individuals per unit area or volume. It is a measure of how crowded a place is, providing a quantitative way to describe the distribution of people. In our case, the population density is given as 560 people per square kilometer. This means that, on average, there are 560 people living within each square kilometer of the circular region. It's important to note that this is an average value; the actual distribution of people may vary within the region due to factors such as geographical features, availability of resources, and infrastructure development. High population density areas often experience challenges related to housing, transportation, and sanitation, while low population density areas may face issues related to access to services and economic opportunities. Understanding population density is therefore crucial for policymakers and planners in making informed decisions about resource allocation and urban development. By accurately calculating population sizes, we can better anticipate the needs of a community and plan for sustainable growth. This involves considering various factors such as the availability of resources, the capacity of infrastructure, and the potential environmental impacts. In the following sections, we will explore the mathematical steps involved in calculating the population of a circular region, demonstrating how the concept of population density is applied in practice. This will provide a solid foundation for understanding more complex population dynamics and their implications for society.

Calculating the Area of the Circular Region

To calculate the total population, we first need to determine the area of the circular region. The formula for the area of a circle is given by:

$$A = \pi r^2$$

where:

• A represents the area of the circle.
• π (pi) is a mathematical constant approximately equal to 3.14159.
• r is the radius of the circle.

In our problem, the radius (r) is given as 13.9 kilometers. Plugging this value into the formula, we get:

$$A = \pi (13.9)^2$$

Now, let's calculate the square of the radius:

$$(13.9)^2 = 13.9 \times 13.9 = 193.21$$

So, the equation becomes:

$$A = \pi \times 193.21$$

Using the approximation of π as 3.14159, we can calculate the area:

$$A = 3.14159 \times 193.21$$

$$A \approx 607.055 ext{ square kilometers}$$

Therefore, the area of the circular region is approximately 607.055 square kilometers. This area represents the total space within which the population is distributed. Knowing the area is a critical step in calculating the total population, as it provides the basis for applying the population density. The area calculation is a fundamental geometric concept that has wide applications in various fields, including land surveying, urban planning, and environmental management. Accurate area calculations are essential for determining land use, estimating resource availability, and assessing environmental impacts. In the context of population studies, the area of a region is a key factor in determining population density and understanding population distribution patterns. In the next section, we will use this calculated area and the given population density to determine the total number of people living in the circular region. This will demonstrate the practical application of geometric principles in population studies and highlight the importance of accurate measurements in such calculations.

Calculating the Total Population

Now that we have the area of the circular region, we can calculate the total population. We know the population density is 560 people per square kilometer. To find the total population, we multiply the area by the population density:

$$ext{Total Population} = ext{Area} \times ext{Population Density}$$

We have the area, which is approximately 607.055 square kilometers, and the population density, which is 560 people per square kilometer. Plugging these values into the formula, we get:

$$ext{Total Population} = 607.055 ext{ km}^2 \times 560 ext{ people/km}^2$$

Now, let's perform the multiplication:

$$ext{Total Population} = 340,000 ext{ (rounded to the nearest person)}$$

$$ext{Total Population} = 339950.8$$

Since we need to round our answer to the nearest person, we look at the decimal part of the result. In this case, the decimal part is .8, which is greater than 0.5, so we round up to the next whole number.

$$ext{Total Population} \approx 339,951 ext{ people}$$

Therefore, the total population living in the circular region is approximately 339,951 people. This calculation demonstrates how population density and area are used to estimate the total number of people in a given region. The result provides valuable information for various purposes, such as resource planning, infrastructure development, and policy making. Understanding the total population is crucial for allocating resources effectively and ensuring the well-being of the community. For instance, knowing the population size helps in determining the number of schools, hospitals, and other essential services needed in the area. It also aids in planning for transportation systems, housing, and other infrastructure projects. In addition, population data is essential for policymakers in making informed decisions about social programs, economic development initiatives, and environmental conservation efforts. The accuracy of the population calculation depends on the precision of the area measurement and the reliability of the population density data. Therefore, it is important to use accurate measurements and up-to-date information to obtain the most reliable estimate of the total population. This ensures that planning and decision-making are based on the best available data, leading to more effective and sustainable outcomes.

Conclusion

In this guide, we have walked through the process of calculating the population within a circular region. We started by understanding the concept of population density and its significance in various fields. We then calculated the area of the circular region using the formula $A = \pi r^2$, where r is the radius. Finally, we multiplied the area by the population density to find the total population. Using a radius of 13.9 kilometers and a population density of 560 people per square kilometer, we determined that approximately 339,951 people live in the circular region. This exercise highlights the practical application of geometric principles in real-world scenarios and demonstrates the importance of accurate calculations in population studies. The ability to calculate population sizes is essential for effective planning and resource allocation, as it provides valuable information for policymakers, urban planners, and environmental scientists. By understanding population distribution patterns, we can better address the needs of communities and ensure sustainable development. The steps outlined in this guide can be applied to various similar problems, allowing you to calculate population sizes in different regions and contexts. Whether you are a student learning about population dynamics or a professional working in a related field, the knowledge and skills gained from this guide will be valuable in your endeavors. The combination of geometric calculations and population density data provides a powerful tool for understanding human distribution and its implications for society and the environment. As we continue to face challenges related to urbanization, resource management, and environmental sustainability, the ability to accurately assess population sizes and densities will become increasingly important. This knowledge empowers us to make informed decisions and create a more equitable and sustainable future for all.

radius 13.9 kilometers population density 560 people per square kilometer, How many people live in that circular region?

How to calculate the population of a circular region with a radius of 13.9 kilometers and a population density of 560 people per square kilometer?