A swimming pool is in the shape of a right circular cylinder with a diameter of 12 ft and a water depth of 5.1 ft. If it costs $3.55 per 1,000 gallons, then what is the cost to fill the pool. Use the conversion 1 gallon = 0.134 cubic ft. Round your answer to two decimal places.

To find the cost to fill the pool, we need to calculate the volume of water it can hold in cubic feet, convert that volume to gallons, and then compute the cost based on the price per 1,000 gallons.

### Step 1: Calculate the volume of the pool in cubic feet
The pool is a right circular cylinder, so its volume can be calculated using the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where:
- $ r $ is the radius of the pool,
- $ h $ is the depth of the water,
- $ \pi $ is approximately 3.14159.

Given that the diameter of the pool is 12 feet, the radius $ r $ is half the diameter:
\[
r = \frac{12}{2} = 6 \text{ ft}
\]
The depth of the water is $ h = 5.1 \text{ ft} $.

Now, we can calculate the volume of the pool:
\[
V = \pi (6)^2 (5.1) = \pi (36)(5.1) = 183.6\pi \text{ cubic feet}
\]
\[
V \approx 183.6 \times 3.14159 = 576.89 \text{ cubic feet}
\]

### Step 2: Convert cubic feet to gallons
We are given the conversion factor:
\[
1 \text{ gallon} = 0.134 \text{ cubic feet}
\]
To find the number of gallons in 576.89 cubic feet, divide the volume by 0.134:
\[
\text{Gallons} = \frac{576.89}{0.134} \approx 4306.64 \text{ gallons}
\]

### Step 3: Calculate the cost
The cost to fill the pool is $3.55 per 1,000 gallons. So, we need to calculate the cost for 4306.64 gallons:
\[
\text{Cost} = \frac{4306.64}{1000} \times 3.55 \approx 4.30664 \times 3.55 = 15.29
\]

### Final Answer:
The cost to fill the pool is approximately **$15.29**.

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Would you like more details or do you have any questions?

Here are five related questions you could explore:
1. What is the cost to fill a similar pool with a diameter of 15 ft?
2. How would the cost change if the water depth increased by 2 feet?
3. How much would it cost to fill a cylindrical tank with a radius of 8 ft and a height of 6 ft?
4. What is the cost to fill a pool if the price per 1,000 gallons rises to $4.00?
5. How many gallons of water would be required if the pool were only 3/4 full?

**Tip:** Always remember to double-check unit conversions when working with different measurements, especially in real-world problems.

A swimming pool is in the shape of a right circular cylinder with a diameter of 12 ft and a water depth of 5.1 ft. If it costs $3.55 per 1,000 gallons, then what is the cost to fill the pool? Use the conversion 1 gallon = 0.134 cubic ft. Round your answer to two decimal places.

Learn how to calculate the cost to fill a cylindrical pool with a diameter of 12 ft and a water depth of 5.1 ft. This detailed solution involves geometry, volume calculations, and unit conversions, with a final cost calculation based on the price per 1,000 gallons. Perfect for students in Grades 9-12.

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