https://file.aiquickdraw.com/mathbot/file/1721846487796yaljbu2u.png

To calculate the volume of the combined shapes in the diagram, we need to determine the volume of both the rectangular prism and the cylinder, then add them together.

### Step 1: Calculate the volume of the rectangular prism

The volume \( V \) of a rectangular prism is given by:
\[ V_{\text{prism}} = \text{length} \times \text{width} \times \text{height} \]

Given dimensions:
- Length = 7 ft
- Width = 4 ft
- Height = 9 ft

So,
\[ V_{\text{prism}} = 7 \times 4 \times 9 = 252 \, \text{ft}^3 \]

### Step 2: Calculate the volume of the cylinder

The volume \( V \) of a cylinder is given by:
\[ V_{\text{cylinder}} = \pi \times r^2 \times h \]

Given dimensions:
- Radius (\( r \)) = 3 ft
- Height (\( h \)) = 6 ft

So,
\[ V_{\text{cylinder}} = \pi \times (3)^2 \times 6 = \pi \times 9 \times 6 = 54\pi \]

Approximating \( \pi \) as 3.14,
\[ V_{\text{cylinder}} \approx 54 \times 3.14 = 169.56 \, \text{ft}^3 \]

### Step 3: Combine the volumes

Adding the volumes of the rectangular prism and the cylinder:
\[ V_{\text{total}} = V_{\text{prism}} + V_{\text{cylinder}} = 252 + 169.56 = 421.56 \, \text{ft}^3 \]

Therefore, the total volume of the combined shapes is approximately \( 421.56 \, \text{ft}^3 \).

Would you like more details or have any questions?

Here are 5 questions you might ask:
1. How do you calculate the surface area of the combined shapes?
2. What is the formula for the volume of a cylinder?
3. How would the volume change if the cylinder's radius was doubled?
4. How do you convert cubic feet to cubic meters?
5. What other shapes can be combined with a rectangular prism to calculate total volume?

**Tip:** Always double-check your measurements and units to ensure accurate calculations.

Learn how to calculate the volume of combined shapes involving a rectangular prism and a cylinder. Step-by-step solution provided with detailed formulas and calculations. Suitable for Grades 7-9.

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