The problem asks to find the volume of the given 3D structure. This shape is a composite solid, which can be divided into two rectangular prisms.

Step 1: Break down the shape

• Top rectangular prism:

  • Length = 10 in
  • Width = 3 in
  • Height = 2 in
  • Volume = $10 \times 3 \times 2 = 60 \, \text{in}^3$

• Bottom rectangular prism:

  • Length = 8 in
  • Width = 3 in
  • Height = 12 in
  • Volume = $8 \times 3 \times 12 = 288 \, \text{in}^3$

Step 2: Add the volumes

• Total Volume = $60 + 288 = 348 \, \text{in}^3$

Final Answer:

The volume of the composite shape is 348 cubic inches.

Would you like further clarifications or detailed diagrams for the solution?

Here are some related questions for further understanding:

1. How do you find the volume of other composite shapes?
2. What is the formula for the volume of a rectangular prism?
3. Can the method used here be applied to cylindrical composite shapes?
4. How would the solution change if the dimensions of one prism were altered?
5. Why is breaking down the composite shape into smaller parts useful?

Tip: Always verify the dimensions and ensure no overlap when calculating the volume of composite shapes.