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Let's break down the problem step by step:

1. The rope goes around the outside of the circular trampoline, so the rope represents the circumference of the trampoline. 

2. The cost of the rope is $2.75 per foot, and the total cost is $104.50.

First, we can calculate how many feet of rope were used by dividing the total cost by the cost per foot:
\[
\text{Length of rope} = \frac{\text{Total cost}}{\text{Cost per foot}} = \frac{104.50}{2.75} \approx 38 \text{ feet}
\]

3. Now, we know the length of the rope is the circumference of the trampoline. The formula for the circumference of a circle is:
\[
C = \pi d
\]
where $C$ is the circumference and $d$ is the diameter.

We can solve for $d$:
\[
d = \frac{C}{\pi} = \frac{38}{\pi} \approx 12.1 \text{ feet}
\]

Rounding to the nearest foot, the diameter of the trampoline is **12 feet**.

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Do you want more details or have any questions? Here are some related questions you might find interesting:

1. How would you calculate the radius instead of the diameter?
2. What would happen if the price per foot of rope increased?
3. How would you solve this problem if the total cost was different?
4. Can you calculate the area of the trampoline with the given diameter?
5. What is the relationship between the diameter and the circumference of any circle?

**Tip:** Always check units and round appropriately when solving practical problems like this one!

A circular trampoline has a padded rope that goes around the outside of the frame. The rope for this trampoline is sold for $2.75 per foot and costs $104.50 before tax. What is the diameter (to the nearest foot) of the trampoline?

Learn how to find the diameter of a circular trampoline using the cost and per-foot price of a rope. This problem involves geometry concepts such as circumference and diameter. Suitable for students in Grades 6-8.

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