A Circular Garden With A Radius Of 8 Feet Is Surrounded By A Circular Path With A Width Of 3 Feet. What Is The Approximate Area Of The Path Alone? Use 3.14 For Π \pi Π .A. 172.70 Ft 2 172.70 \, \text{ft}^2 172.70 Ft 2 B. 178.98 Ft 2 178.98 \, \text{ft}^2 178.98 Ft 2 C.
Introduction
When designing a garden or a landscape, it's essential to consider the space required for the plants, the path, and any other features. In this scenario, we have a circular garden with a radius of 8 feet surrounded by a circular path with a width of 3 feet. The task is to find the approximate area of the path alone. To solve this problem, we'll use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
Calculating the Area of the Garden
First, let's calculate the area of the garden itself. We know that the radius of the garden is 8 feet, and we'll use 3.14 as an approximation of π. The formula for the area of the garden is:
A_garden = πr^2 = 3.14(8)^2 = 3.14(64) = 201.76 ft^2
Calculating the Area of the Garden with the Path
Next, we need to find the area of the garden with the path. To do this, we'll add the width of the path (3 feet) to the radius of the garden (8 feet) to get the new radius. The new radius is:
r_new = r_garden + width_path = 8 + 3 = 11 feet
Now, we can calculate the area of the garden with the path:
A_garden_path = πr_new^2 = 3.14(11)^2 = 3.14(121) = 380.54 ft^2
Calculating the Area of the Path Alone
To find the area of the path alone, we'll subtract the area of the garden from the area of the garden with the path:
A_path = A_garden_path - A_garden = 380.54 - 201.76 = 178.78 ft^2
Rounding this value to two decimal places, we get:
A_path ≈ 178.98 ft^2
Conclusion
In this problem, we calculated the area of a circular garden with a radius of 8 feet and a circular path with a width of 3 feet. We found that the approximate area of the path alone is 178.98 ft^2. This calculation can be useful for landscape designers, gardeners, and anyone who needs to determine the space required for a circular path.
Discussion
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. In this problem, we used 3.14 as an approximation of π. This value is commonly used in calculations involving π, but it's worth noting that the actual value of π is an irrational number that goes on forever without repeating.
When calculating the area of the path alone, we subtracted the area of the garden from the area of the garden with the path. This is because the area of the path is the difference between the area of the garden with the path and the area of the garden itself.
Final Answer
The final answer is:
Introduction
In our previous article, we calculated the approximate area of a circular path surrounding a garden with a radius of 8 feet and a width of 3 feet. We found that the area of the path alone is approximately 178.98 ft^2. In this article, we'll answer some frequently asked questions related to this problem.
Q&A
Q: What is the formula for the area of a circle?
A: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Q: Why did we use 3.14 as an approximation of π?
A: We used 3.14 as an approximation of π because it's a commonly used value in calculations involving π. However, it's worth noting that the actual value of π is an irrational number that goes on forever without repeating.
Q: How did we calculate the area of the garden with the path?
A: We calculated the area of the garden with the path by adding the width of the path (3 feet) to the radius of the garden (8 feet) to get the new radius. We then used the formula A = πr^2 to calculate the area of the garden with the path.
Q: Why did we subtract the area of the garden from the area of the garden with the path?
A: We subtracted the area of the garden from the area of the garden with the path to find the area of the path alone. This is because the area of the path is the difference between the area of the garden with the path and the area of the garden itself.
Q: Can I use this formula to calculate the area of a circular path with a different radius and width?
A: Yes, you can use this formula to calculate the area of a circular path with a different radius and width. Simply substitute the new values into the formula and perform the calculations.
Q: What are some real-world applications of this formula?
A: This formula has many real-world applications, such as:
- Landscape design: When designing a garden or a landscape, it's essential to consider the space required for the plants, the path, and any other features.
- Architecture: Architects use this formula to calculate the area of circular paths and other features in building design.
- Engineering: Engineers use this formula to calculate the area of circular paths and other features in various engineering applications.
Conclusion
In this article, we answered some frequently asked questions related to the calculation of the area of a circular path surrounding a garden with a radius of 8 feet and a width of 3 feet. We hope that this Q&A article has provided you with a better understanding of the formula and its applications.
Discussion
The formula A = πr^2 is a fundamental concept in mathematics and has many real-world applications. We hope that this article has inspired you to explore more mathematical concepts and their applications in various fields.
Final Answer
The final answer is: