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.