Finding the Volume of Composite Rectangular Prisms - WORKSHEET for ... - Free Printable

Looking at the fourth composite rectangular prism (bottom right), I can see it's an L-shaped figure similar to the first one, but oriented differently. The dimensions shown are 6 ft for the length of the main section, 5 ft for the height of the main section, and 3 ft for the height of the smaller section that extends out.

The width (depth) appears to be the same for both sections, though it's not explicitly labeled in this cropped view. Based on the pattern from the other shapes, I would expect the width to be consistent across the entire composite shape.

Now that I've examined all four composite prisms, I'll calculate the volume for each one by breaking them down into simpler rectangular prisms and summing their volumes.

For the first composite prism (top left):
- Base section: L = 10 in, W = 3 in, H = 4 in
- Vertical section: L = ? in, W = 3 in, H = 4 in

I need to determine the length of the vertical section. Looking at the diagram again, since it's an L-shape and the total length is 10 in, and there's no indication of how much of that length the vertical section occupies, I'll need to make an assumption. In typical problems like this, if not specified otherwise, we often assume the vertical section spans the full width, but here it's positioned on top of the base. Without more information, I'll assume the vertical section has the same length as the base (10 in), which would make it a simple rectangular prism on top, not truly L-shaped. However, looking at the shape more carefully, it appears the vertical section might be narrower.

Actually, re-examining the first shape, I believe the vertical section is positioned on the right side of the base, and its length is not specified. This is problematic. Let me look at the image again to see if I missed any dimension.

Wait, I think I need to reconsider. In many such problems, when a composite shape is shown without all dimensions specified, we assume that the missing dimensions can be inferred from the overall dimensions and the visible parts. For the first shape, if the total length is 10 in and the vertical section is on top of the base, it's likely that the vertical section has the same length as the base, making the entire shape a rectangular prism with a portion cut out or added. But that doesn't match the L-shape.

Actually, looking at it again, I think the vertical section's length is meant to be the same as the width (3 in), making it a cube-like section on top. But that doesn't seem right either.

Let me try a different approach. Perhaps the first shape is meant to be divided into two parts: a large rectangular prism (10 in × 3 in × 4 in) and a smaller one on top of it (let's say x in × 3 in × 4 in). But without knowing x, I can't calculate it.

Wait, I think I made an error in my initial assessment. Looking at the first shape again, I believe the "10 in" is the total length, and the vertical section is positioned such that its length is not the full 10 in. However, since no other length is given for the vertical section, I'll have to assume it spans the full length, making the shape a rectangular prism of 10 in × 3 in × 8 in, but that doesn't match the L-shape shown.

Actually, I think the most reasonable assumption is that the vertical section has the same length as the base, which is 10 in, and the L-shape is created by the height difference. So the volume would be the volume of the entire rectangular prism minus the volume of the missing part, but that's not what's shown.

Let me reconsider the first shape. It appears to be composed of two rectangular prisms:
1. A base prism: 10 in (length) × 3 in (width) × 4 in (height)
2. A top prism: ? in (length) × 3 in (width) × 4 in (height)

Since the top prism is sitting on top of the base and appears to extend from the right edge, I'll assume its length is the same as the width, which is 3 in. This is a common convention in such problems when dimensions are not fully specified.

So for the first shape:
- Base: V1 = 10 × 3 × 4 = 120 in³
- Top: V2 = 3 × 3 × 4 = 36 in³
- Total: V = 120 + 36 = 156 in³

For the second shape (top right):
- Bottom: V1 = 8 × 7 × 2 = 112 ft³
- Top: V2 = 8 × 7 × 4 = 224 ft³
- Total: V = 112 + 224 = 336 ft³

For the third shape (bottom left):
- Bottom: V1 = 6 × 4 × 3 = 72 cm³
- Top: V2 = 6 × 4 × 5 = 120 cm³
- Total: V = 72 + 120 = 192 cm³

For the fourth shape (bottom right):
- Main section: V1 = 6 × ? × 5 = ? ft³
- Smaller section: V2 = 3 × ? × 3 = ? ft³

I need the width for the fourth shape. Looking at the diagram, the width isn't specified, but it should be the same for both sections. Since it's not given, I'll assume it's 3 ft, matching the height of the smaller section, as is common in such problems.

So for the fourth shape:
- Main section: V1 = 6 × 3 × 5 = 90 ft³
- Smaller section: V2 = 3 × 3 × 3 = 27 ft³
- Total: V = 90 + 27 = 117 ft³

Wait, I think I made an error in assuming the width for the fourth shape. Let me reconsider. In the fourth shape, the smaller section is shown extending out, and its height is 3 ft, but the width (depth) should be the same as the main section. Since it's not specified, and to be consistent with the other shapes, I'll assume the width is 3 ft.

Actually, looking at the fourth shape more carefully, I believe the width is meant to be the same as the length of the smaller section, which is 3 ft. So my calculation stands.

Let me summarize the volumes:

1. First shape: 156 in³
2. Second shape: 336 ft³
3. Third shape: 192 cm³
4. Fourth shape: 117 ft³

However, I'm not entirely confident about the assumptions I made for the first and fourth shapes. In a real classroom setting, the teacher would provide all necessary dimensions or clarify the assumptions. Since this is an exercise, I'll proceed with these calculations.

The final answer is:
- First composite prism: 156 in³
- Second composite prism: 336 ft³
- Third composite prism: 192 cm³
- Fourth composite prism: 117 ft³