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Let's analyze the problem:

We have two cylindrical containers:

1. **Container A**:
   - Diameter = 14 feet
   - Height = 11 feet
   - Thus, the radius \( r_A = \frac{14}{2} = 7 \) feet.

2. **Container B**:
   - Diameter = 10 feet
   - Height = 19 feet
   - Thus, the radius \( r_B = \frac{10}{2} = 5 \) feet.

Both are filled and emptied via the following process:
- **Container A** is initially full, and water is pumped into **Container B** until Container B is completely full.
  
We need to determine what percentage of **Container A** is empty once **Container B** is full.

### Volume of Cylinders Formula:
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]

Now, let's calculate the volumes:

1. **Volume of Container A**:
   \[
   V_A = \pi (7^2)(11) = \pi (49)(11) = 539 \pi \, \text{cubic feet}
   \]

2. **Volume of Container B**:
   \[
   V_B = \pi (5^2)(19) = \pi (25)(19) = 475 \pi \, \text{cubic feet}
   \]

### Water Transfer:
The water from **Container A** fills **Container B** entirely. So, **Container A** will lose the volume of water that matches the volume of **Container B**.

Thus, the remaining volume of water in **Container A** after pumping is:
\[
V_{\text{remaining}} = V_A - V_B = 539 \pi - 475 \pi = 64 \pi \, \text{cubic feet}
\]

### Percentage Empty:
The percentage of **Container A** that is empty is given by:
\[
\% \, \text{empty} = \frac{V_B}{V_A} \times 100 = \frac{475 \pi}{539 \pi} \times 100 = \frac{475}{539} \times 100
\]
\[
\% \, \text{empty} \approx 88.1\%
\]

So, to the nearest tenth, **88.1%** of **Container A** will be empty after the pumping is complete.

Let me know if you'd like any further clarifications or more details! Here are some related questions you might consider:

1. What would happen if the height of Container B were reduced?
2. How would the result change if Container B had a different shape, such as a rectangular prism?
3. What if Container A started with only half its capacity filled?
4. How does the volume formula for a cylinder compare to other 3D shapes?
5. Can you generalize the percentage calculation for different-sized containers?

**Tip:** Always ensure you compare volumes by using the correct units and shapes, especially when solving fluid or capacity problems.

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 feet and a height of 11 feet. Container B has a diameter of 10 feet and a height of 19 feet. Container A is full of water, and the water is pumped into Container B until Container B is completely full. To the nearest tenth, what is the percent of Container A that is empty after the pumping is complete?

This problem involves two cylindrical containers, A and B, where water is transferred from one to the other. Learn how to calculate the percentage of Container A that is empty after water is transferred into Container B. Key concepts include cylinder volume and percentage calculations. Suitable for students in Grades 9-12.

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