The problem requires finding the volume of the given solid, which consists of two rectangular prisms combined. Let's break it down step by step.

Step 1: Identify the two parts of the solid

1. Bottom rectangular prism:

   • Length: 10 cm
   • Width: 3 cm
   • Height: 3 cm

   Volume = $\text{length} \times \text{width} \times \text{height}$
   $V_{\text{bottom}} = 10 \times 3 \times 3 = 90 \, \text{cm}^3$

2. Top rectangular prism:

   • Length: 7 cm
   • Width: 3 cm
   • Height: 4 cm

   Volume = $\text{length} \times \text{width} \times \text{height}$
   $V_{\text{top}} = 7 \times 3 \times 4 = 84 \, \text{cm}^3$

Step 2: Add the volumes of the two prisms

Total volume = $V_{\text{bottom}} + V_{\text{top}}$
$V_{\text{total}} = 90 + 84 = 174 \, \text{cm}^3$

Final Answer:

The volume of the solid is 174 cm³.

Would you like further details or explanation? Here are five related questions to expand on this topic:

1. How would the total volume change if the top prism had a different height?
2. What is the formula for the surface area of this solid?
3. Can you calculate the volume if one dimension of the bottom prism is doubled?
4. How do we determine the center of mass of a composite solid like this?
5. What happens to the total volume if the two prisms are combined differently?

Tip: When solving composite volume problems, always break the solid into simpler shapes to simplify calculations.