To determine how many flowers are needed to surround the circular garden, we first need to calculate the circumference of the garden and then divide that by the spacing between the flowers.

Step 1: Calculate the Circumference of the Garden

The formula for the circumference of a circle is:

$C = 2 \pi r$

Where:

• $C$ is the circumference,
• $\pi$ is approximately 3.14,
• $r$ is the radius of the circle.

Given:

• The radius $r = 125 \, \text{ft}$.

Using $\pi = 3.14$, we can compute the circumference:

$C = 2 \times 3.14 \times 125 = 785 \, \text{ft}$

Step 2: Convert the Circumference to Inches

Since the flowers are spaced every 4 inches, it's easier to convert the circumference from feet to inches. There are 12 inches in a foot, so:

$785 \, \text{ft} \times 12 = 9420 \, \text{inches}$

Step 3: Determine How Many Flowers Are Needed

The flowers are spaced every 4 inches, so the number of flowers needed is:

$\frac{\text{Circumference in inches}}{\text{Spacing between flowers}} = \frac{9420}{4} = 2355 \, \text{flowers}$

Final Answer:

You need 2,355 flowers to surround the circular garden.

Would you like any further details or clarifications on this?

Here are some related questions:

1. How would the result change if the spacing between flowers were increased to 6 inches?
2. What if the garden had a different radius, say 100 feet—how many flowers would be needed?
3. How can we calculate the area of the garden based on the given radius?
4. How does the use of 3.14 as an approximation for pi affect the precision of the result?
5. How would the number of flowers change if the spacing between them were reduced to 2 inches?

Tip: Always convert all units to the same measurement before performing calculations (e.g., inches in this case) to ensure consistency in your work.