Sections of wrought iron pipe, having an inside diameter of 4", are filled with concrete and used for posts to support the main floor girder in the basement of a residence. If these posts are 8'-0" long, and there are 6 in all, how many cubic feet of concrete are required for the job?

To determine the amount of concrete needed for these 6 posts, we can start by calculating the volume of concrete required for one post and then multiply by 6.

### Given Data:
1. **Inside diameter of the pipe (d)** = 4 inches
2. **Length of each post (h)** = 8 feet
3. **Number of posts** = 6

### Step-by-Step Solution:

1. **Convert Diameter to Feet:**
   \[
   d = 4 \text{ inches} = \frac{4}{12} \text{ feet} = \frac{1}{3} \text{ feet}
   \]

2. **Calculate Radius in Feet:**
   Radius \( r \) is half of the diameter:
   \[
   r = \frac{d}{2} = \frac{1}{3} \div 2 = \frac{1}{6} \text{ feet}
   \]

3. **Volume of Concrete in One Post:**
   Since each post is cylindrical, the volume \( V \) of concrete required for one post can be calculated using the formula for the volume of a cylinder:
   \[
   V = \pi r^2 h
   \]
   Substituting the values:
   \[
   V = \pi \left(\frac{1}{6}\right)^2 \times 8
   \]
   \[
   V = \pi \times \frac{1}{36} \times 8 = \frac{8\pi}{36} = \frac{2\pi}{9} \text{ cubic feet}
   \]

4. **Total Volume for 6 Posts:**
   \[
   \text{Total volume} = 6 \times \frac{2\pi}{9} = \frac{12\pi}{9} = \frac{4\pi}{3} \text{ cubic feet}
   \]

5. **Approximate Value:**
   Using \( \pi \approx 3.1416 \):
   \[
   \text{Total volume} \approx \frac{4 \times 3.1416}{3} \approx 4.1888 \text{ cubic feet}
   \]

### Answer:
Approximately **4.19 cubic feet** of concrete are required for the job.

Would you like additional details, or have any questions?

---

1. What would the volume be if the pipe's inside diameter was different?
2. How does changing the length of each post affect the total concrete volume?
3. What is the effect on volume if fewer posts are used?
4. How does the wall thickness of the pipe affect the volume calculation?
5. How would we convert this answer to cubic inches?

**Tip:** When dealing with circular or cylindrical volumes, always ensure units are consistent (e.g., converting inches to feet when necessary).

This guide explains how to calculate the concrete volume needed to fill six 8-foot posts with an inside diameter of 4 inches. Learn how to use the cylinder volume formula and unit conversions, ideal for geometry practice for Grades 9-10.

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