1. yes 2. the radius of cylinder A is 4 feet

Great! Now that we know the radius of **Cylinder A** is 4 feet, we can calculate its height using the fact that the volumes of both cylinders are equal.

### Given Information:
- **Cylinder A**:
  - Radius, \(r_A = 4\) feet
  - Height, \(h_A\) (to be found)

- **Cylinder B**:
  - Radius, \(r_B = 2\) cm
  - Height, \(h_B = 6\) cm
  - Volume, \(V_B = 24\pi\) cubic cm

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

### Step-by-Step Solution:

#### Step 1: Find the Volume of Cylinder B

We already calculated the volume of **Cylinder B**:
\[
V_B = \pi r_B^2 h_B = \pi (2)^2 \times 6 = 24\pi \, \text{cm}^3
\]

#### Step 2: Set the Volumes Equal

Since the volumes of Cylinder A and Cylinder B are equal:

\[
V_A = V_B
\]

\[
\pi r_A^2 h_A = 24\pi
\]

#### Step 3: Plug in the Known Values for Cylinder A

\[
\pi (4)^2 h_A = 24\pi
\]

Simplify the equation:

\[
16\pi h_A = 24\pi
\]

Divide both sides by \(\pi\):

\[
16h_A = 24
\]

#### Step 4: Solve for the Height of Cylinder A

\[
h_A = \frac{24}{16} = \frac{3}{2} = 1.5 \, \text{feet}
\]

### Answer:

- The height of **Cylinder A** is **1.5 feet**.
- The height of **Cylinder B** is already given as **6 cm**.

Would you like to know more about related concepts or have any further questions?

Here are five additional questions to explore this topic further:

1. How do you convert the units from feet to centimeters if needed for consistency in measurements?
2. What are the implications of doubling the height or radius of a cylinder on its volume?
3. How does changing the radius while keeping the volume constant affect the height of a cylinder?
4. Can the formula for the volume of a cylinder be used to find the radius if the height and volume are known?
5. How do different units (such as feet and centimeters) impact volume calculations when converting?

**Tip:** Always double-check your units and conversion factors when performing volume calculations, especially when comparing two shapes or objects.

Learn how to calculate the height of Cylinder A when given its radius and the equality of volumes with Cylinder B. Detailed step-by-step solution included. Suitable for students in Grades 7-9.

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