The problem involves a circular garden with a radius of 20 yards and a surrounding path (an annular region) with a width of 6 yards. The task is to determine how many bags of sand are required to cover the path, given that each bag covers 8 square yards, and π should be approximated as 3.14.

Steps:

1. Find the area of the entire circle including the path (outer radius).

   • Outer radius = 20 yards (garden radius) + 6 yards (path width) = 26 yards.
   • Area of the entire circle = π * (outer radius)² = 3.14 * (26)² = 3.14 * 676 = 2123.44 square yards.

2. Find the area of the garden (inner circle).

   • Inner radius = 20 yards.
   • Area of the inner circle = π * (inner radius)² = 3.14 * (20)² = 3.14 * 400 = 1256 square yards.

3. Find the area of the path by subtracting the inner circle's area from the outer circle's area.

   • Area of the path = 2123.44 - 1256 = 867.44 square yards.

4. Calculate the number of bags of sand required.

   • Each bag covers 8 square yards.
   • Number of bags = Area of the path / 8 = 867.44 / 8 = 108.43 bags.

   Since the number of bags must be a whole number, round up to the next whole number:

   • Number of bags = 109.

Final Answer:

The gardener will need 109 bags of sand.

Would you like further clarification on any step or more details?

Here are 5 related questions:

1. How would the result change if the path width was 8 yards instead of 6 yards?
2. Can we calculate the cost if each bag costs a certain amount of money?
3. How do we calculate the area of a sector of a circle?
4. How would the solution differ if the sand coverage per bag was in different units (e.g., square meters)?
5. How do we apply this method to calculate the area of a semicircular garden path?

Tip: Always check the problem for rounding rules, especially when dealing with discrete quantities like bags.