How many cubic yards of concrete are in a light pole caisson having a diameter of 24 inches and a depth of 6 feet?



To calculate the volume of concrete in the light pole caisson, we treat it as a cylinder and use the formula for the volume of a cylinder:

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

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height (or depth), and
- \( \pi \) is approximately 3.14159.

### Step 1: Convert dimensions to feet
- Diameter = 24 inches = 2 feet, so the radius \( r \) is half of that: \( r = 1 \) foot.
- Depth \( h = 6 \) feet.

### Step 2: Calculate the volume in cubic feet
\[
V = \pi \times (1^2) \times 6 = 3.14159 \times 1 \times 6 = 18.8496 \text{ cubic feet}
\]

### Step 3: Convert cubic feet to cubic yards
Since 1 cubic yard = 27 cubic feet, we divide the volume in cubic feet by 27:

\[
\text{Volume in cubic yards} = \frac{18.8496}{27} \approx 0.698 \text{ cubic yards}
\]

### Final Answer:
The volume of concrete is approximately **0.698 cubic yards**.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How would the volume change if the depth was doubled?
2. What is the effect of increasing the diameter by 50% on the volume?
3. How do you calculate the cost of concrete if the price per cubic yard is known?
4. How does the shape of the caisson affect the structural integrity of the pole?
5. What other factors should be considered in designing a concrete caisson?

**Tip:** Always ensure unit consistency (feet, inches, yards) when calculating volumes to avoid errors.

How many cubic yards of concrete are in a light pole caisson having a diameter of 24 inches and a depth of 6 feet?

Learn how to calculate the volume of concrete required for a light pole caisson with a diameter of 24 inches and a depth of 6 feet. This problem uses the formula for the volume of a cylinder and covers unit conversions from feet to yards. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation