___ yd3 of concrete will be required for 14 parking lot light pole standards that are 32 inches in diameter and 8 feet tall.

To find how much concrete (in cubic yards) is needed for the light pole standards, we can treat each light pole standard as a cylinder and calculate its volume. The formula for the volume \(V\) of a cylinder is:

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

Where:
- \(r\) is the radius (half of the diameter),
- \(h\) is the height,
- \(\pi \approx 3.1416\).

### Step 1: Convert dimensions to consistent units
Since the problem asks for the volume in cubic **yards**, we need to convert the measurements to yards:
- **Diameter** of each pole = 32 inches → radius \(r = \frac{32}{2} = 16\) inches.
    - 1 yard = 36 inches, so the radius in yards is:
    \[
    r = \frac{16}{36} \approx 0.444 \text{ yards}
    \]
- **Height** of each pole = 8 feet.
    - 1 yard = 3 feet, so the height in yards is:
    \[
    h = \frac{8}{3} \approx 2.667 \text{ yards}
    \]

### Step 2: Calculate the volume of one pole
Using the formula for the volume of a cylinder:
\[
V = \pi r^2 h = 3.1416 \times (0.444)^2 \times 2.667
\]
Let's calculate this.

The volume of one light pole standard is approximately 1.655 cubic yards.

### Step 3: Calculate the total volume for 14 poles
To find the total amount of concrete required for all 14 poles, we multiply the volume of one pole by 14:

\[
V_{\text{total}} = 14 \times 1.655 = 23.17 \text{ cubic yards}
\]

Thus, approximately **23.17 cubic yards** of concrete will be required for the 14 parking lot light pole standards.

Would you like more details on any part of the solution?

Here are 5 related questions:
1. How do you convert between different units of length (inches, feet, yards)?
2. What is the general formula for the volume of a cylinder?
3. How does the volume of a cylinder change when you double the radius or the height?
4. What other shapes can you use to model structures like light poles?
5. How do you calculate the weight of concrete needed, given the density?

**Tip**: When dealing with volume calculations, always ensure units are consistent throughout the calculation!

yd3 of concrete will be required for 14 parking lot light pole standards that are 32 inches in diameter and 8 feet tall.

Find out how to calculate the amount of concrete required for 14 parking lot light pole standards, each 32 inches in diameter and 8 feet tall. Learn how to use the cylindrical volume formula and convert units from inches and feet to cubic yards. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation