Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 20 feet. Container B has a diameter of 20 feet and a height of 10 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?

To solve this problem, we'll first calculate the volumes of both containers and then determine how much of Container B remains empty after water from Container A is transferred into it.

### Step 1: Calculate the Volume of Each Cylinder
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base.
- \( h \) is the height.

### Step 2: Find the Volume of Container A
- Diameter of Container A: 10 feet, so the radius \( r_A = \frac{10}{2} = 5 \) feet.
- Height of Container A: 20 feet.

\[
V_A = \pi (5)^2 (20) = \pi \times 25 \times 20 = 500\pi \ \text{cubic feet}
\]

### Step 3: Find the Volume of Container B
- Diameter of Container B: 20 feet, so the radius \( r_B = \frac{20}{2} = 10 \) feet.
- Height of Container B: 10 feet.

\[
V_B = \pi (10)^2 (10) = \pi \times 100 \times 10 = 1000\pi \ \text{cubic feet}
\]

### Step 4: Determine the Amount of Water in Container B After Transfer
Since Container A is emptied and all its water is transferred to Container B:
- Water transferred from Container A = \( 500\pi \ \text{cubic feet} \).

The new volume of water in Container B is \( 500\pi \ \text{cubic feet} \).

### Step 5: Calculate the Percent of Container B That Is Empty
Now, we need to find out what percent of Container B remains empty after the transfer.

1. The volume of Container B is \( 1000\pi \ \text{cubic feet} \).
2. The volume filled with water is \( 500\pi \ \text{cubic feet} \).
3. The empty volume of Container B is \( 1000\pi - 500\pi = 500\pi \).

To find the percentage of Container B that is empty, use the formula:

\[
\text{Percent empty} = \left(\frac{\text{Empty volume}}{\text{Total volume}}\right) \times 100
\]
\[
\text{Percent empty} = \left(\frac{500\pi}{1000\pi}\right) \times 100 = \left(\frac{500}{1000}\right) \times 100 = 50\%
\]

### Final Answer
After the water from Container A is pumped into Container B, **50% of Container B remains empty**.

Would you like to see a breakdown of any step, or have further questions? Here are some related problems:

1. How would the result change if the heights of the containers were doubled?
2. What if the radius of Container B were halved?
3. How much time would it take to pump all the water if the pump rate was 10 cubic feet per minute?
4. What is the weight of the water transferred if 1 cubic foot of water weighs approximately 62.4 pounds?
5. How would the problem change if Container A only started half-full?

**Tip:** For problems involving volumes of similar shapes, always ensure dimensions are in consistent units for accurate calculations.

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 20 feet. Container B has a diameter of 20 feet and a height of 10 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?

Solve a geometric problem involving the volume of two cylindrical containers. Container A (10ft diameter, 20ft height) is full of water and transferred to Container B (20ft diameter, 10ft height). Calculate what percent of Container B remains empty after the transfer using cylinder volume formulas. Suitable for Grades 9-10.

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