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.

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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 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 calculate the approximate area of the path alone. To achieve this, 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 Circular Garden

First, let's calculate the area of the circular garden. We know that the radius of the garden is 8 feet, and we'll use 3.14 as an approximation of π. Plugging in the values, we get:

A = πr^2 A = 3.14(8)^2 A = 3.14(64) A = 201.76 ft^2

Calculating the Area of the Larger Circle (Garden + Path)

Next, we need to calculate the area of the larger circle that includes both the garden and 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 radius of the larger circle:

Radius of the larger circle = 8 + 3 = 11 feet

Now, we can calculate the area of the larger circle using the same formula:

A = πr^2 A = 3.14(11)^2 A = 3.14(121) A = 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 larger circle:

Area of the path alone = Area of the larger circle - Area of the garden = 380.54 - 201.76 = 178.78 ft^2

Rounding this value to two decimal places, we get approximately 178.98 ft^2.

Conclusion

In this scenario, we calculated the approximate area of the circular path alone by first finding the area of the circular garden and the larger circle that includes both the garden and the path. We then subtracted the area of the garden from the area of the larger circle to get the area of the path alone. The result is approximately 178.98 ft^2.

Discussion

The calculation of the area of the path alone is a simple yet essential task in landscape design. By understanding the formulas and calculations involved, you can create beautiful and functional outdoor spaces that meet your needs and preferences.

Frequently Asked Questions

  • 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: What is the radius of the circular garden? A: The radius of the circular garden is 8 feet.
  • Q: What is the width of the circular path? A: The width of the circular path is 3 feet.
  • Q: What is the approximate area of the path alone? A: The approximate area of the path alone is 178.98 ft^2.

References

Introduction

In our previous article, we explored the calculation of the approximate area of the circular path alone surrounding a circular garden with a radius of 8 feet and a path width of 3 feet. We used the formula for the area of a circle, A = πr^2, to find the area of the garden and the larger circle that includes both the garden and the path. We then subtracted the area of the garden from the area of the larger circle to get the area of the path alone.

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: What is the radius of the circular garden?

A: The radius of the circular garden is 8 feet.

Q: What is the width of the circular path?

A: The width of the circular path is 3 feet.

Q: How do I calculate the area of the garden?

A: To calculate the area of the garden, you can use the formula A = πr^2, where A is the area and r is the radius. Plugging in the values, we get:

A = πr^2 A = 3.14(8)^2 A = 3.14(64) A = 201.76 ft^2

Q: How do I calculate the area of the larger circle (garden + path)?

A: To calculate the area of the larger circle, you need to add the width of the path (3 feet) to the radius of the garden (8 feet) to get the radius of the larger circle:

Radius of the larger circle = 8 + 3 = 11 feet

Now, you can calculate the area of the larger circle using the same formula:

A = πr^2 A = 3.14(11)^2 A = 3.14(121) A = 380.54 ft^2

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

A: To find the area of the path alone, you'll subtract the area of the garden from the area of the larger circle:

Area of the path alone = Area of the larger circle - Area of the garden = 380.54 - 201.76 = 178.78 ft^2

Rounding this value to two decimal places, we get approximately 178.98 ft^2.

Q: What is the approximate area of the path alone?

A: The approximate area of the path alone is 178.98 ft^2.

Q: Can I use a different value for π?

A: Yes, you can use a different value for π, but keep in mind that the result will be slightly different. For example, if you use 3.14159 instead of 3.14, the result will be:

Area of the path alone = 178.98 ft^2 (using 3.14) Area of the path alone = 179.03 ft^2 (using 3.14159)

Q: Can I use this formula for other shapes?

A: No, this formula is specifically for calculating the area of a circle. If you need to calculate the area of other shapes, you'll need to use different formulas.

Q: Can I use this formula for other units of measurement?

A: Yes, you can use this formula for other units of measurement, such as inches or meters, as long as you convert the values to the same unit.

Conclusion

In this Q&A article, we've covered various questions related to the calculation of the approximate area of the circular path alone surrounding a circular garden with a radius of 8 feet and a path width of 3 feet. We've used the formula for the area of a circle, A = πr^2, to find the area of the garden and the larger circle that includes both the garden and the path. We've then subtracted the area of the garden from the area of the larger circle to get the area of the path alone.

Discussion

The calculation of the area of the path alone is a simple yet essential task in landscape design. By understanding the formulas and calculations involved, you can create beautiful and functional outdoor spaces that meet your needs and preferences.

Frequently Asked Questions

  • 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: What is the radius of the circular garden? A: The radius of the circular garden is 8 feet.
  • Q: What is the width of the circular path? A: The width of the circular path is 3 feet.
  • Q: What is the approximate area of the path alone? A: The approximate area of the path alone is 178.98 ft^2.

References