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The problem involves a cylindrical water tank filled to 75% of its total volume. We need to determine the height of the water level based on the provided volume formula for a cylinder.

### Key Information:
- The total volume \( V \) of a cylinder is given by:
  \[
  V = \pi r^2 h
  \]
  where \( r \) is the radius of the cylinder and \( h \) is its height.
  
- The radius \( r \) is 6 inches.
- We are asked to find the height of the water when the tank is filled to 75% of its volume.

### Step-by-Step Solution:

1. **Total Volume of the Tank:**
   Using the volume formula for a cylinder, the total volume \( V_{\text{total}} \) is:
   \[
   V_{\text{total}} = \pi r^2 h = \pi (6)^2 h = 36\pi h
   \]

2. **Volume of Water (75% of Total Volume):**
   Since the tank is filled to 75% of its volume, the volume of water \( V_{\text{water}} \) is:
   \[
   V_{\text{water}} = 0.75 \times V_{\text{total}} = 0.75 \times 36\pi h = 27\pi h
   \]

3. **Formula for the Height of the Water:**
   The height of the water level can be found by setting up the volume formula for the water, where the water's volume is also a cylinder but with height \( h_{\text{water}} \) instead of \( h \). So:
   \[
   V_{\text{water}} = \pi r^2 h_{\text{water}}
   \]
   Substituting the radius \( r = 6 \):
   \[
   V_{\text{water}} = \pi (6)^2 h_{\text{water}} = 36\pi h_{\text{water}}
   \]

4. **Solving for \( h_{\text{water}} \):**
   Set the two expressions for the water's volume equal to each other:
   \[
   27\pi h = 36\pi h_{\text{water}}
   \]
   Simplifying:
   \[
   h_{\text{water}} = \frac{27\pi h}{36\pi} = \frac{3h}{4}
   \]

Thus, the height of the water level is \( \frac{3h}{4} \), where \( h \) is the total height of the tank.

### Checking the Options:
The correct answer should match the expression for \( h_{\text{water}} \). Since the height is \( \frac{3h}{4} \), we can conclude that the correct answer is not directly listed in terms of \( h \), but it relates to this.

### Do you need more details, or should I clarify something further?

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Here are some questions you might want to explore based on this problem:

1. How would the height of the water change if the tank were filled to 50% instead of 75%?
2. What would be the height of the water if the radius were doubled?
3. How does the volume of a cylinder change if the height is halved but the radius is doubled?
4. How can the formula for the volume of a cylinder be derived geometrically?
5. What is the impact of increasing both the radius and height on the volume?

**Tip**: When solving volume-related problems for cylindrical shapes, always make sure to account for the correct proportional relationships between radius, height, and volume!

A circular cylindrical water tank is filled with water to 75 percent of its total volume of V cubic inches. The radius of the tank is 6 inches, and the height of the tank is h inches. Which of the following represents the height, in inches, of the water in the tank? (Note: The volume of a cylinder with radius r and height h is given by πr²h.)

Learn how to calculate the height of water in a cylindrical tank filled to 75% of its volume. The problem involves key geometric concepts, including the volume formula for a cylinder and understanding proportional relationships. Suitable for students in Grades 9-12.

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