Mr Townes created a 2foot wide garden path around a circular garden. The radius of the garden is 7 feet. He wants to cover the path in stones. If mr. Townes needs 1 bag of stones for every 5 square feet of path, how many bags of stones will he need to cover his garden path?

50.9

81 pi - 49 pi = 32pi sq. ft . or 100.48 sq. ft.

Mr. Townes will need 21 bags of stone to be sure to cover his garden path

To find the area of the garden path, we need to subtract the area of the inner circle from the area of the outer circle. Here's how you can calculate it:

1. Find the area of the outer circle:
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius.
So, the area of the outer circle can be calculated as A_outer = π(7ft)^2.

2. Find the area of the inner circle:
The radius of the inner circle can be obtained by subtracting the width of the garden path from the radius of the outer circle.
So, the radius of the inner circle is (7ft - 2ft) = 5ft.
Now, calculate the area of the inner circle as A_inner = π(5ft)^2.

3. Calculate the area of the garden path:
The area of the garden path is the difference between the area of the outer circle and the area of the inner circle:
A_path = A_outer - A_inner.

4. Determine the number of bags of stones needed:
Given that 1 bag of stones covers 5 square feet of path, divide the area of the garden path (A_path) by 5 to determine the number of bags needed.
Number of bags = A_path / 5.

Now, let's calculate the number of bags required:

A_outer = π(7ft)^2 = 49π ft^2 (using the area formula for a circle)

A_inner = π(5ft)^2 = 25π ft^2 (using the area formula for a circle)

A_path = A_outer - A_inner = 49π ft^2 - 25π ft^2 = 24π ft^2

Number of bags = A_path / 5 = 24π ft^2 / 5 ≈ 15.08 bags

Therefore, Mr. Townes will need approximately 15.08 bags of stones to cover his garden path. However, since we cannot have a fraction of a bag, he would need to purchase at least 16 bags to completely cover the garden path.

area path= area outer-area inner

= PI (9^2 - 7^2)= PI*(81-49) figure that out.

Now, bags of stones=1bag/5 * area