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The posts in the illustration are set in concrete. All post and castings are cylindrical. How many cubic feet of earth are excavated for setting both identical posts A and D.

To solve the problem, we need to calculate the volume of earth excavated for posts \( A \) and \( D \), which are both set in cylindrical holes.

### Given Data:
- **Diameter of each excavation (for posts A and D):** \( 10 \) inches
- **Depth of each excavation:** \( 3'2" \) (which equals \( 3 \times 12 + 2 = 38 \) inches)

### Steps:
1. **Convert all measurements to feet** to find the volume in cubic feet:
   - Diameter = \( 10 \) inches = \( \frac{10}{12} \) feet = \( 0.833 \) feet.
   - Radius \( r \) = \( \frac{0.833}{2} \approx 0.4165 \) feet.
   - Depth = \( 38 \) inches = \( \frac{38}{12} \approx 3.167 \) feet.

2. **Calculate the volume of one cylindrical hole** using the formula:
   \[
   V = \pi r^2 h
   \]
   where:
   - \( r \approx 0.4165 \) feet
   - \( h \approx 3.167 \) feet

3. **Compute the volume for each post**:
   \[
   V = \pi \times (0.4165)^2 \times 3.167
   \]

4. **Double the volume** to account for both posts \( A \) and \( D \).

Let’s compute this.The total volume of earth excavated for setting both posts \( A \) and \( D \) is approximately \( 3.45 \) cubic feet.

Would you like more details on the calculations or have further questions?

Here are some related questions that might interest you:
1. How would the volume change if the diameter of the excavation increased?
2. What would be the volume if posts \( B \) and \( C \) were excavated as well?
3. How do you calculate the volume if the excavation has a different shape, like a rectangular prism?
4. What formula is used to calculate the volume of a cylindrical hole?
5. How would you calculate the weight of concrete needed to fill each excavation?

**Tip:** When dealing with volume calculations, always ensure all measurements are in the same units before applying formulas.

The posts in the illustration are set in concrete. All post and castings are cylindrical. How many cubic feet of earth are excavated for setting both identical posts A and D?

Learn how to calculate the cubic feet of earth excavated for setting cylindrical posts A and D in concrete. This problem includes geometry concepts, specifically calculating the volume of cylindrical holes with given diameters and depths. Suitable for high school students in Grades 9-12.

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