Dewayne is welding up two 10 inch pipes to each other.  Each of his welding rods makes a 0.90 inch bead.  The number of welding rods in a 5 lbs. box can be found by taking the denominator of the diameter of the welding rod and multiplying it by 4.15.  For example a 5lbs. box of 1/16" welding rods has approximately 16*4.15
66 rods in a 5 lbs. box.  If a 5lb box of 1/8 welding rods is used for the weld, and a 5lb box costs $18.39, how much does each pass around the weld cost just in welding rods?

Let's break this problem down step by step:

### Step 1: Find the number of rods in a 5 lb box of 1/8" welding rods
According to the problem, the number of welding rods in a 5 lb box is calculated by multiplying the denominator of the welding rod diameter by 4.15.

The diameter of the rod is $ \frac{1}{8} $ inches. Therefore:
\[
\text{Number of rods} = 8 \times 4.15 = 33.2
\]
So, there are approximately 33 rods in a 5 lb box.

### Step 2: Determine how much welding a single rod can complete
Each welding rod makes a bead of 0.90 inches.

### Step 3: Find the circumference of the pipe
Since Dewayne is welding 10-inch pipes, the circumference of the pipe is the length of each pass:
\[
\text{Circumference} = \pi \times \text{Diameter} = \pi \times 10 \approx 31.42 \text{ inches}
\]

### Step 4: Calculate the number of rods required for one pass
One rod can weld 0.90 inches, so the number of rods needed for one pass is:
\[
\text{Rods per pass} = \frac{\text{Circumference}}{\text{Bead length per rod}} = \frac{31.42}{0.90} \approx 34.91
\]
This means Dewayne needs approximately 35 rods for one pass.

### Step 5: Find the cost of rods for one pass
The cost of a 5 lb box of rods is $18.39, and there are approximately 33 rods in a box. Therefore, the cost per rod is:
\[
\text{Cost per rod} = \frac{18.39}{33} \approx 0.56 \text{ dollars}
\]

Now, multiply the number of rods per pass by the cost per rod:
\[
\text{Cost per pass} = 35 \times 0.56 = 19.60 \text{ dollars}
\]

### Final Answer:
The cost of each pass around the weld, just in welding rods, is approximately **$19.60**.

---

Would you like further details on this, or do you have any questions?

Here are 5 follow-up questions:
1. How many passes would be needed to complete the weld, and what would the total cost be?
2. How does the cost change if Dewayne uses a different rod diameter, like 3/32"?
3. What is the total cost of welding if Dewayne uses 2 boxes of rods?
4. What is the efficiency of the welding process if some of the rods are wasted?
5. How can the price of rods affect the overall cost of a large welding project?

**Tip:** When working with circumferences, always use a few decimal places of accuracy for $\pi$, such as 3.1416, to ensure precision.

Dewayne is welding up two 10 inch pipes to each other. Each of his welding rods makes a 0.90 inch bead. The number of welding rods in a 5 lbs. box can be found by taking the denominator of the diameter of the welding rod and multiplying it by 4.15. For example, a 5lbs. box of 1/16" welding rods has approximately 16*4.15 = 66 rods in a 5 lbs. box. If a 5lb box of 1/8 welding rods is used for the weld, and a 5lb box costs $18.39, how much does each pass around the weld cost just in welding rods?

Calculate the cost of welding rods for each pass around a 10-inch pipe weld. Learn how to use the diameter of welding rods, pipe circumference, and rod costs to determine the overall cost for a welding project. This problem involves algebra, unit conversion, and geometry concepts. Ideal for Grades 9-12.

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