How many cubic yards of concrete are needed for a foundation that is 14-6" in diameter and 2'-6" deep?

To determine the volume of concrete needed for the foundation, we'll treat it as a cylinder and use the volume formula for a cylinder:

\[
V = \pi r^2 h
\]

where:
- \( r \) is the radius,
- \( h \) is the height (or depth in this case).

### Step 1: Convert the Measurements to Feet
1. **Diameter** = 14 feet 6 inches
   - Convert to feet: 14 feet + \( \frac{6}{12} \) feet = 14.5 feet.
   - **Radius** \( r = \frac{\text{diameter}}{2} = \frac{14.5}{2} = 7.25 \) feet.

2. **Depth** = 2 feet 6 inches
   - Convert to feet: 2 feet + \( \frac{6}{12} \) feet = 2.5 feet.

### Step 2: Substitute the Values into the Volume Formula
\[
V = \pi (7.25)^2 \times 2.5
\]
Calculating this:

1. \( 7.25^2 = 52.5625 \)
2. \( \pi \times 52.5625 \approx 165.13 \)
3. \( 165.13 \times 2.5 = 412.825 \) cubic feet

### Step 3: Convert Cubic Feet to Cubic Yards
There are 27 cubic feet in a cubic yard, so:
\[
\text{Cubic yards} = \frac{412.825}{27} \approx 15.29
\]

### Answer
You would need approximately **15.29 cubic yards of concrete** for the foundation.

Would you like additional details or have any questions?

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1. How do you calculate the volume of different shapes?
2. What are the unit conversions commonly used in construction?
3. How does the volume calculation differ if the foundation were a rectangular prism instead of a cylinder?
4. What adjustments are needed if the foundation's depth changes?
5. How does adding or subtracting inches to diameter or depth impact the total concrete required?

**Tip:** Always double-check unit conversions when dealing with both feet and inches to ensure accuracy.

Determine the cubic yards of concrete needed for a cylindrical foundation with a diameter of 14 feet 6 inches and depth of 2 feet 6 inches. This guide covers volume calculation and unit conversions, ideal for students in Grades 9-12.

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