Volume of Compound 3D Shapes worksheet with six geometric figures and dimensions for calculating volume.

I will solve the problem by calculating the volume of each compound 3D shape. The general approach is to break each complex shape into simpler rectangular prisms, calculate the volume of each part, and then add or subtract them as needed.

Let me start with Shape 1.

Shape 1:
This shape can be divided into two rectangular prisms:
- Bottom prism: 4 cm (length) × 2 cm (width) × 2 cm (height)
- Top prism: 2 cm (length) × 2 cm (width) × 2 cm (height)

Volume = (4 × 2 × 2) + (2 × 2 × 2) = 16 + 8 = 24 cm³

Shape 2:
This L-shaped prism can be seen as a large rectangular prism with a smaller one removed, or as two separate prisms.
I'll use the two-prism method:
- Left vertical prism: 5 cm (height) × 2 cm (width) × 2 cm (depth) = 20 cm³
- Right horizontal prism: 4 cm (length) × 2 cm (width) × 2 cm (height) = 16 cm³
Wait, let me reconsider this. Looking at the dimensions, it's better to think of it as:
- Bottom part: 6 cm (length) × 2 cm (height) × 2 cm (width) = 24 cm³
- Top left part: 4 cm (length) × 3 cm (height) × 2 cm (width) = 24 cm³
Total volume = 24 + 24 = 48 cm³

Actually, let me double-check this. The total height is 5 cm, and the top section is 4 cm long and 3 cm high (since 5-2=3). So:
- Bottom rectangular prism: 6 cm × 2 cm × 2 cm = 24 cm³
- Top rectangular prism: 4 cm × 3 cm × 2 cm = 24 cm³
Total volume = 24 + 24 = 48 cm³

Shape 3:
This shape can be divided into two rectangular prisms:
- Bottom prism: 5 cm (length) × 3 cm (width) × 2 cm (height) = 30 cm³
- Top prism: 3 cm (length) × 3 cm (width) × 2 cm (height) = 18 cm³
Total volume = 30 + 18 = 48 cm³

Shape 4:
This shape can be divided into three parts or calculated as a whole.
I'll divide it into three rectangular prisms:
- Bottom left: 2 cm × 2 cm × 1 cm = 4 cm³ (assuming depth is 1 cm based on the top part)
Wait, I need to be more careful. Let me look at the dimensions again.
The shape has a total width of 3 cm, height of 4 cm, and depth of 2 cm.
I can see it as:
- Bottom part: 3 cm × 2 cm × 1 cm = 6 cm³ (if the bottom step is 1 cm high)
- Middle part: 2 cm × 2 cm × 1 cm = 4 cm³ (the middle step)
- Top part: 2 cm × 2 cm × 1 cm = 4 cm³ (the top step)
But this doesn't seem right based on the drawing.

Looking at it differently:
- The entire shape can be seen as a 3 cm × 4 cm × 2 cm rectangular prism minus some parts, but that's complicated.
- Better to divide it into:
- Bottom rectangular prism: 3 cm (length) × 2 cm (height) × 2 cm (width) = 12 cm³
- Top rectangular prism: 2 cm (length) × 2 cm (height) × 2 cm (width) = 8 cm³
Total volume = 12 + 8 = 20 cm³

Shape 5:
This L-shaped object can be divided into two rectangular prisms:
- Vertical part: 2 cm (width) × 5 cm (height) × 2 cm (depth) = 20 cm³
- Horizontal part: 7 cm (length) × 1 cm (height) × 3 cm (width) = 21 cm³
Wait, I need to check the dimensions again. The horizontal part appears to be 7 cm long, 3 cm wide, and 1 cm high. The vertical part is 5 cm high, 2 cm wide, and 2 cm deep (assuming the depth is consistent).
Total volume = 20 + 21 = 41 cm³

Actually, let me reconsider. The vertical part might have a different depth. Looking at the drawing, the vertical part seems to be 2 cm wide, 5 cm high, and 2 cm deep. The horizontal part is 7 cm long, 3 cm wide, and 1 cm high. But they share a common area, so I need to make sure I'm not double-counting.
Since they meet at a corner, there's no overlap in volume calculation.
Total volume = (2 × 5 × 2) + (7 × 3 × 1) = 20 + 21 = 41 cm³

Shape 6:
This is a large rectangular prism with a smaller rectangular prism removed from it.
- Large prism: 8 cm (length) × 6 cm (height) × 4 cm (width) = 192 cm³
- Small prism (removed): 4 cm (length) × 2 cm (height) × 4 cm (width) = 32 cm³
Total volume = 192 - 32 = 160 cm³

Now, let me summarize the answers:

1) 24 cm³
2) 48 cm³
3) 48 cm³
4) 20 cm³
5) 41 cm³
6) 160 cm³