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

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Introduction

When designing a garden or a landscape, it's essential to consider the space and layout to ensure that it's both aesthetically pleasing and functional. One common design element is a circular garden surrounded by a circular path. In this article, we'll explore how to calculate the approximate area of the circular path alone, given the radius of the garden and the width of the path.

Calculating the Area of a Circle

To calculate the area of a circle, we use the formula:

A = πr^2

where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given Information

We are given a circular garden with a radius of 8 feet, surrounded by a circular path with a width of 3 feet. To calculate the area of the path alone, we need to find the area of the larger circle (including the garden and the path) and subtract the area of the smaller circle (the garden alone).

Calculating the Radius of the Larger Circle

The radius of the larger circle is the sum of the radius of the garden and the width of the path:

r_large = r_garden + w_path = 8 ft + 3 ft = 11 ft

Calculating the Area of the Larger Circle

Using the formula for the area of a circle, we can calculate the area of the larger circle:

A_large = πr_large^2 = 3.14(11 ft)^2 = 3.14(121 ft^2) = 380.54 ft^2

Calculating the Area of the Smaller Circle

The radius of the smaller circle is the radius of the garden alone:

r_small = r_garden = 8 ft

Using the formula for the area of a circle, we can calculate the area of the smaller circle:

A_small = πr_small^2 = 3.14(8 ft)^2 = 3.14(64 ft^2) = 201.06 ft^2

Calculating the Area of the Path Alone

To find the area of the path alone, we subtract the area of the smaller circle from the area of the larger circle:

A_path = A_large - A_small = 380.54 ft^2 - 201.06 ft^2 = 179.48 ft^2

Rounding to two decimal places, we get:

A_path ≈ 178.98 ft^2

Conclusion

In this article, we calculated the approximate area of a circular path alone, given the radius of the garden and the width of the path. We used the formula for the area of a circle and performed the necessary calculations to find the area of the path alone. The result is approximately 178.98 ft^2.

Discussion

The calculation of the area of a circular path alone is an essential aspect of landscape design and architecture. By understanding how to calculate this area, designers and architects can create more efficient and aesthetically pleasing designs. The result of this calculation can also be used to determine the amount of materials needed for the path, such as concrete or gravel.

References

Related Topics

  • Calculating the area of a rectangle
  • Calculating the area of a triangle
  • Calculating the perimeter of a circle
  • Landscape design and architecture
  • Circular paths in architecture and design

Introduction

In our previous article, we explored how to calculate the approximate area of a circular path alone, given the radius of the garden and the width of the path. In this article, we'll answer some frequently asked questions related to this topic.

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

A: The formula for calculating the area of a circle is:

A = πr^2

where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Q: How do I calculate the radius of the larger circle?

A: To calculate the radius of the larger circle, you need to add the radius of the garden and the width of the path:

r_large = r_garden + w_path

Q: What is the difference between the area of the larger circle and the area of the smaller circle?

A: The area of the larger circle is the area of the garden and the path combined, while the area of the smaller circle is the area of the garden alone. By subtracting the area of the smaller circle from the area of the larger circle, you can find the area of the path alone.

Q: Can I use a calculator to calculate the area of the path alone?

A: Yes, you can use a calculator to calculate the area of the path alone. Simply enter the values for the radius of the garden and the width of the path, and the calculator will give you the result.

Q: What if I have a circular garden with a radius of 10 feet and a circular path with a width of 4 feet?

A: To calculate the area of the path alone, you would need to follow the same steps as before:

  1. Calculate the radius of the larger circle: r_large = r_garden + w_path = 10 ft + 4 ft = 14 ft
  2. Calculate the area of the larger circle: A_large = πr_large^2 = 3.14(14 ft)^2 = 615.36 ft^2
  3. Calculate the area of the smaller circle: A_small = πr_small^2 = 3.14(10 ft)^2 = 314 ft^2
  4. Calculate the area of the path alone: A_path = A_large - A_small = 615.36 ft^2 - 314 ft^2 = 301.36 ft^2

Q: Can I use this formula to calculate the area of a circular path with a different shape?

A: No, this formula is specifically designed for circular paths. If you have a circular path with a different shape, you will need to use a different formula.

Q: What if I have a circular garden with a radius of 12 feet and a circular path with a width of 5 feet?

A: To calculate the area of the path alone, you would need to follow the same steps as before:

  1. Calculate the radius of the larger circle: r_large = r_garden + w_path = 12 ft + 5 ft = 17 ft
  2. Calculate the area of the larger circle: A_large = πr_large^2 = 3.14(17 ft)^2 = 907.96 ft^2
  3. Calculate the area of the smaller circle: A_small = πr_small^2 = 3.14(12 ft)^2 = 452.16 ft^2
  4. Calculate the area of the path alone: A_path = A_large - A_small = 907.96 ft^2 - 452.16 ft^2 = 455.80 ft^2

Q: Can I use this formula to calculate the area of a circular path with a negative radius?

A: No, this formula is not designed to handle negative radii. If you have a circular path with a negative radius, you will need to use a different formula.

Conclusion

In this article, we answered some frequently asked questions related to calculating the area of a circular path alone. We hope that this Q&A article has been helpful in clarifying any confusion and providing additional information on this topic.

Discussion

The calculation of the area of a circular path alone is an essential aspect of landscape design and architecture. By understanding how to calculate this area, designers and architects can create more efficient and aesthetically pleasing designs. The result of this calculation can also be used to determine the amount of materials needed for the path, such as concrete or gravel.

References

Related Topics

  • Calculating the area of a rectangle
  • Calculating the area of a triangle
  • Calculating the perimeter of a circle
  • Landscape design and architecture
  • Circular paths in architecture and design