Surface area calculation for a 3D shape composed of two cubes.

Let me work through this problem step by step to find the total surface area that needs to be painted.

Step 1: Understanding the object
- We have two cubes stacked on top of each other
- Larger cube: side = 3.3 cm
- Smaller cube: side = 1.2 cm (sitting on top of the larger cube)

Step 2: What surfaces need to be painted?
When painting, we need to paint all EXTERNAL surfaces. The contact area between the two cubes is NOT painted because it's hidden inside.

Step 3: Calculate for the larger cube
- Area of one face = 3.3 × 3.3 = 10.89 cm²
- The larger cube has 6 faces, but:
- The bottom face: painted ✓
- 4 side faces: painted ✓
- Top face: partially covered by small cube

So for the larger cube:
- Bottom + 4 sides = 5 faces = 5 × 10.89 = 54.45 cm²
- Top face exposed area = total top - area covered by small cube
= 10.89 - (1.2 × 1.2)
= 10.89 - 1.44
= 9.45 cm²

Total for larger cube = 54.45 + 9.45 = 63.90 cm²

Step 4: Calculate for the smaller cube
- Area of one face = 1.2 × 1.2 = 1.44 cm²
- The smaller cube has 6 faces, but:
- Bottom face: NOT painted (touching large cube)
- Top + 4 sides = 5 faces are painted

Area for smaller cube = 5 × 1.44 = 7.20 cm²

Step 5: Total area to paint
Total = 63.90 + 7.20 = 71.10 cm²

Let me verify my calculation:
- Large cube: 5 complete faces (54.45) + partial top (9.45) = 63.90 ✓
- Small cube: 5 faces (7.20) ✓
- Total: 63.90 + 7.20 = 71.10 ✓

Final Answer: 71.10 cm²