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.

Mar 10, 2025 by ADMIN 269 views

A Circular Garden with a Circular Path: Calculating the Area of the Path Alone

Introduction

When designing a garden or a landscape, it's essential to consider the space required for the plants, pathways, and other features. In this article, we'll explore how to calculate the area of a circular path surrounding a circular garden. We'll use a specific example to demonstrate the calculation process and provide a step-by-step guide to help you understand the concept.

The Problem

A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. We need 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'll use the formula A = πr^2, where r is the radius of the garden, which is 8 feet.

A = πr^2
A = 3.14 \times (8)^2
A = 3.14 \times 64
A = 201.06 \, \text{ft}^2

Calculating the Area of the Garden and the Path

Next, we need to calculate the area of the garden and the path combined. 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 of the garden and the path combined.

\text{New radius} = 8 + 3
\text{New radius} = 11 \, \text{ft}

Now, we'll use the formula A = πr^2 to calculate the area of the garden and the path combined.

A = πr^2
A = 3.14 \times (11)^2
A = 3.14 \times 121
A = 380.54 \, \text{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 and the path combined.

\text{Area of the path alone} = \text{Area of the garden and the path} - \text{Area of the garden}
\text{Area of the path alone} = 380.54 - 201.06
\text{Area of the path alone} = 179.48 \, \text{ft}^2

Conclusion

In this article, we calculated the approximate area of a circular path surrounding a circular garden. We used the formula A = πr^2 to find the area of the garden, the area of the garden and the path combined, and finally, the area of the path alone. The approximate area of the path alone is 179.48 ft^2.

Discussion

The calculation process involves finding the area of the garden, the area of the garden and the path combined, and finally, the area of the path alone. The formula A = πr^2 is used to calculate the area of each circle. The width of the path is added to the radius of the garden to get the new radius of the garden and the path combined.

Final Answer

The final answer is $\boxed{179.48 \, \text{ft}^2}$ .

Comparison with the Options

Let's compare our final answer with the options provided:

A. $172.70 \, \text{ft}^2$ B. $178.98 \, \text{ft}^2$ C. $179.48 \, \text{ft}^2$

Our final answer, $179.48 \, \text{ft}^2$ , is closest to option C.

Introduction

In our previous article, we explored how to calculate the area of a circular path surrounding a circular garden. We used a specific example to demonstrate the calculation process and provided a step-by-step guide to help you understand the concept. In this article, we'll answer some frequently asked questions related to the topic.

Q&A

Q1: What is the formula for calculating the area of a circle?

A1: The formula for calculating the area of a circle is A = πr^2, where A is the area and r is the radius.

Q2: How do I calculate the area of the garden and the path combined?

A2: To calculate the area of the garden and the path combined, you need to add the width of the path to the radius of the garden to get the new radius of the garden and the path combined. Then, use the formula A = πr^2 to calculate the area.

Q3: How do I calculate the area of the path alone?

A3: To calculate the area of the path alone, you need to subtract the area of the garden from the area of the garden and the path combined.

Q4: What if the path is not circular? Can I still use the same formula?

A4: No, if the path is not circular, you cannot use the same formula. The formula A = πr^2 is only applicable to circular shapes. You would need to use a different formula or method to calculate the area of the path.

Q5: Can I use a calculator to calculate the area of the garden and the path?

A5: Yes, you can use a calculator to calculate the area of the garden and the path. However, make sure to use the correct formula and values to get the accurate result.

Q6: What if I have a rectangular garden with a circular path? Can I still use the same formula?

A6: No, if you have a rectangular garden with a circular path, you cannot use the same formula. The formula A = πr^2 is only applicable to circular shapes. You would need to use a different formula or method to calculate the area of the path.

Q7: Can I use the formula A = πr^2 to calculate the area of a sphere?

A7: No, the formula A = πr^2 is only applicable to circular shapes, not spheres. To calculate the area of a sphere, you would need to use a different formula, such as A = 4πr^2.

Q8: What if I have a garden with multiple paths? Can I still use the same formula?

A8: No, if you have a garden with multiple paths, you cannot use the same formula. You would need to calculate the area of each path separately and then add them together to get the total area of the paths.