To solve the problem, we need to determine how many flowers, spaced every 3 inches, are needed to surround a circular garden with a 200-ft radius, using $\pi = 3.14$.

Step-by-Step Solution:

1. Calculate the Circumference of the Circle: The formula for the circumference $C$ of a circle is: $C = 2 \pi r$ where $r$ is the radius and $\pi = 3.14$. Here, the radius $r$ is 200 feet.

   So, $C = 2 \times 3.14 \times 200 = 1256 \text{ feet}$

2. Convert Feet to Inches: Since the flowers are spaced every 3 inches, we need to convert the circumference from feet to inches. There are 12 inches in a foot, so: $C = 1256 \times 12 = 15072 \text{ inches}$

3. Determine the Number of Flowers: The number of flowers can be found by dividing the total circumference in inches by the spacing between the flowers (3 inches): $\text{Number of flowers} = \frac{15072}{3} = 5024$

Final Answer:

5024 flowers are needed to surround the circular garden.

Would you like more details on any part of this solution, or have any questions?

Here are 5 related questions for practice:

1. What would be the circumference of a circle with a radius of 150 feet?
2. If the flowers were spaced 6 inches apart, how many flowers would be needed?
3. How would the number of flowers change if the radius was 300 feet?
4. What is the area of the circular garden with a 200-ft radius?
5. How many flowers would be needed if the garden was a square with a perimeter of 1256 feet?

Tip: Always ensure you convert units (like feet to inches) when dealing with different scales in a problem.