Electric utility poles in the form of right cylinders are made out of wood that costs $11.76 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 20 ft. Round your answer to the nearest cent.

To calculate the cost of the utility pole, we first need to find its volume and then multiply that by the cost per cubic foot.

### Step 1: Find the volume of the cylindrical utility pole

The formula for the volume $ V $ of a cylinder is:

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

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

#### Given dataTo calculate the cost of the utility pole, we first need to find its volume and then multiply that by the cost per cubic foot.

### Step 1: Find the volume of the cylindrical utility pole

The formula for the volume $ V $ of a cylinder is:

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

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

#### Given 
- Diameter of the pole $ = 1.5 \, \text{ft} $, so the radius $ r = \frac{1.5}{2} = 0.75 \, \text{ft} $,
- Height $ h = 20 \, \text{ft} $,
- Cost per cubic foot = $11.76.

Now, we can calculate the volume of the pole:

\[
V = \pi (0.75)^2 \times 20 = \pi \times 0.5625 \times 20
\]

\[
V \approx 3.1416 \times 0.5625 \times 20 \approx 35.343 \, \text{cubic feet}
\]

### Step 2: Calculate the cost of the utility pole

The cost is calculated by multiplying the volume by the cost per cubic foot:

\[
\text{Cost} = 35.343 \, \text{cubic feet} \times 11.76 \, \text{dollars/cubic foot}
\]

\[
\text{Cost} \approx 415.24 \, \text{dollars}
\]

### Final Answer:
The cost of the utility pole is approximately **$415.24**.

Would you like more details or have any questions? Here are a few related questions to deepen your understanding:

1. How would the cost change if the height of the pole increased by 10 feet?
2. What is the cost if the diameter doubled, keeping the height the same?
3. How would the volume change if the diameter was reduced to 1 ft?
4. How do we calculate the surface area of the cylinder instead of the volume?
5. What is the impact on cost if the price per cubic foot increased to $15?

**Tip:** In any geometric problem involving cylinders, always verify whether you're dealing with volume (3D space) or surface area (outer surface).

Learn how to calculate the cost of an electric utility pole in the shape of a right cylinder with a diameter of 1.5 ft and height of 20 ft. Using the volume of a cylinder formula and the cost per cubic foot, we determine the total cost of the pole. Ideal for students in Grades 9-11.

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