Calculating the Area of a Fish Pond Using Perimeter

Imagine you're faced with a unique challenge of determining the area of a circular fish pond using the perimeter of barbed wire. In this article, we'll explore the mathematical concepts needed to solve this problem, using the given perimeter to find both the radius and subsequently the area of the pond. This journey will not only provide a practical solution but also highlight the importance of understanding fundamental geometry.

Understanding the Given Information and the Problem

We are given that a barbed wire with a total length of 176 meters was used to fence a circular fish pond twice. This means the total perimeter of the pond is (176 , text{m}).

Step-by-Step Solution

To find the area of the circular fish pond, we need to determine its radius, which requires us to first find the circumference of the single pond. Given that the barbed wire was used to fence the pond twice, we can halve the total length:

(frac{176 , text{m}}{2} 88 , text{m})

This 88 meters is the circumference of the fish pond. The formula for the circumference of a circle is:

(C 2 pi r)

Where (C) is the circumference, (r) is the radius, and (pi) is approximately 3.1416. Solving for (r) gives us:

(88 2 times 3.1416 times r)

(88 6.2832 times r)

(r frac{88}{6.2832} approx 14 , text{m})

Now that we have the radius, we can find the area of the circle using the formula:

(A pi r^2)

(A 3.1416 times (14 , text{m})^2)

(A 3.1416 times 196 , text{m}^2)

(A approx 615.75 , text{m}^2)

Conclusion

The area of the fish pond is approximately (615.75 , text{m}^2). If the barbed wire was used twice, the area would remain the same. This exercise in geometry teaches us the importance of breaking down complex problems into simpler, more manageable steps. Whether you encounter a similar problem in your homework or in a real-life scenario, understanding these fundamental concepts can be invaluable.

Relevance to Real-World Applications

The real-world application of this problem is significant in various fields such as agriculture, urban planning, and environmental management. Understanding the area of circular spaces can help in planning water usage, managing resources, and ensuring ecological balance.

Additional Resources

For more detailed explanations and additional practice problems, consider exploring online resources such as Khan Academy, MIT OpenCourseWare, and interactive geometry websites. These platforms offer comprehensive guides and exercises to enhance your understanding of geometry and its practical applications.