Calculating the Area of the Path

Oct 13, 2025 by wbrum.org 93 views

Introduction

When designing a garden or a landscape, it's essential to consider the area surrounding a circular flower bed. In this scenario, we have a flower bed with a diameter of 70m, surrounded by a path that is 10m wide. The task is to calculate the area of this path and then determine the cost of tilling it, given that the cost of tilling per square meter is 15rs.

Calculating the Area of the Path

To calculate the area of the path, we need to find the area of the larger circle (including the flower bed and the path) and then subtract the area of the flower bed itself.

Step 1: Find the Radius of the Larger Circle

The diameter of the flower bed is 70m, so the radius is half of that, which is 35m. Since the path is 10m wide, we need to add this width to the radius to get the radius of the larger circle.

Radius of the larger circle = Radius of the flower bed + Width of the path
= 35m + 10m
= 45m

Step 2: Calculate the Area of the Larger Circle

Now that we have the radius of the larger circle, we can calculate its area using the formula for the area of a circle:

Area of the larger circle = πr²
= π(45m)²
= 6359.75m²

Step 3: Calculate the Area of the Flower Bed

We already know the radius of the flower bed, which is 35m. We can use this to calculate its area:

Area of the flower bed = πr²
= π(35m)²
= 3841.88m²

Step 4: Calculate the Area of the Path

Now that we have the area of the larger circle and the area of the flower bed, we can subtract the two to get the area of the path:

Area of the path = Area of the larger circle - Area of the flower bed
= 6359.75m² - 3841.88m²
= 2517.87m²

Calculating the Cost of Tilling the Path

Now that we have the area of the path, we can calculate the cost of tilling it by multiplying the area by the cost of tilling per square meter:

Cost of tilling the path = Area of the path x Cost of tilling per square meter
= 2517.87m² x 15rs/m²
= 37692.30rs

Conclusion

In this scenario, we calculated the area of a path surrounding a circular flower bed with a diameter of 70m and a path that is 10m wide. We then determined the cost of tilling the path, given that the cost of tilling per square meter is 15rs. The area of the path is approximately 2517.87m², and the cost of tilling it is approximately 37692.30rs.

Frequently Asked Questions

What is the formula for calculating the area of a circle? The formula for calculating the area of a circle is πr², where r is the radius of the circle.
How do I calculate the area of a path surrounding a circular flower bed? To calculate the area of a path surrounding a circular flower bed, you need to find the area of the larger circle (including the flower bed and the path) and then subtract the area of the flower bed itself.
What is the cost of tilling per square meter? The cost of tilling per square meter is 15rs.

References

[1] Wikipedia: Circle
[2] Math Open Reference: Circle
[3] Online Calculator: Area of a Circle

Introduction

In our previous article, we discussed how to calculate the area of a path surrounding a circular flower bed. We provided a step-by-step guide on how to find the area of the path and then determined the cost of tilling it. In this article, we will answer some frequently asked questions related to this topic.

Q&A

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

A: The formula for calculating the area of a circle is πr², where r is the radius of the circle.

Q: How do I calculate the area of a path surrounding a circular flower bed?

A: To calculate the area of a path surrounding a circular flower bed, you need to find the area of the larger circle (including the flower bed and the path) and then subtract the area of the flower bed itself.

Q: What is the radius of the larger circle?

A: The radius of the larger circle is the sum of the radius of the flower bed and the width of the path. In our previous example, the radius of the flower bed was 35m and the width of the path was 10m, so the radius of the larger circle was 45m.

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

A: To calculate the area of the larger circle, you can use the formula πr², where r is the radius of the larger circle.

Q: What is the cost of tilling per square meter?

A: The cost of tilling per square meter is 15rs.

Q: How do I calculate the cost of tilling the path?

A: To calculate the cost of tilling the path, you need to multiply the area of the path by the cost of tilling per square meter.

Q: What if the path is not a perfect circle?

A: If the path is not a perfect circle, you can use the same formula to calculate the area of the path, but you will need to use the average radius of the path.

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

A: Yes, you can use a calculator to calculate the area of the path. You can also use online calculators or software to make the calculation easier.

Q: What if I have a rectangular flower bed instead of a circular one?

A: If you have a rectangular flower bed, you can calculate the area of the path by finding the area of the larger rectangle (including the flower bed and the path) and then subtracting the area of the flower bed itself.

Conclusion

In this article, we answered some frequently asked questions related to calculating the area of a path surrounding a circular flower bed. We provided step-by-step guides and formulas to help you understand the concept better. If you have any more questions or need further clarification, please don't hesitate to ask.

Frequently Asked Questions

What is the formula for calculating the area of a circle? The formula for calculating the area of a circle is πr², where r is the radius of the circle.
How do I calculate the area of a path surrounding a circular flower bed? To calculate the area of a path surrounding a circular flower bed, you need to find the area of the larger circle (including the flower bed and the path) and then subtract the area of the flower bed itself.
What is the cost of tilling per square meter? The cost of tilling per square meter is 15rs.

References

[1] Wikipedia: Circle
[2] Math Open Reference: Circle
[3] Online Calculator: Area of a Circle