Find the volume of each composite figure by breaking it into parts and adding the volumes.

Let’s solve each part step by step. We’ll find the volume of each composite figure by breaking it into two rectangular prisms, calculating their volumes separately, then adding them together.

---

Part a:

This shape is made of two blocks stacked vertically.

- Top block (part 1):
Dimensions: length = 10 m, width = 6 m, height = 3 m
Volume = 10 × 6 × 3 = 180 m³

- Bottom block (part 2):
The bottom block has a larger base but same depth? Wait — look carefully.

Actually, looking at the diagram:

The entire front face shows:
- Total height = 9 m
- Top part height = 3 m → so bottom part height = 9 - 3 = 6 m
- Bottom block dimensions: length = 9 m, width = 6 m, height = 6 m? But wait — the top block sits on part of the bottom block.

Actually, from the dashed lines and labels:

Top block: 10 m (length) × 6 m (width) × 3 m (height) → that’s clear.

Bottom block: It extends further in length? No — actually, the bottom block is wider in length? Let me re-read.

Wait — the diagram says:

For part a:

Left side: total height 9 m, with top section labeled 3 m high.

Front view: bottom block has length 9 m, top block has length 10 m? That doesn’t make sense unless they’re offset.

Actually, looking again — probably the top block is sitting on the left part of the bottom block.

But the label “10 m” is on the top block’s length, and “9 m” is on the bottom block’s length? That would mean the top block sticks out? But that contradicts typical problems.

Wait — perhaps I misread. Let me check standard interpretation.

Actually, in such diagrams, often the top block is smaller or aligned. But here:

Looking at the numbers:

Top block: 10 m (front length), 6 m (depth), 3 m (height)

Bottom block: 9 m (front length), 6 m (depth), 6 m (height)? But then how does 10 m fit on 9 m?

Ah — maybe the 10 m is the depth? No, the diagram labels:

On top block: “10 m” along the front edge, “6 m” going back (depth), “3 m” vertical.

On bottom block: “9 m” along front, “6 m” depth, and total height 9 m, with top 3 m, so bottom height 6 m.

But if top block is 10 m long and bottom is 9 m long, that means the top block overhangs? Possible, but unusual.

Alternatively — perhaps the 10 m is the depth? Let me think differently.

Wait — in many textbooks, for such L-shaped or stepped figures, we break into two rectangles.

Another way: Perhaps the bottom block is 9 m (length) × 6 m (width) × 6 m (height)

And the top block is placed on top of it, but only covering part? But the top block is labeled 10 m — which is longer than 9 m? That can't be.

Unless... the 10 m is not length but something else.

Look at the diagram description:

It says:

a.
Top block: 10 m (probably length), 6 m (width/depth), 3 m (height)
Bottom block: 9 m (length), 6 m (width/depth), and since total height is 9 m and top is 3 m, bottom height is 6 m.

But 10 > 9 — so if both have same depth 6 m, then top block must extend beyond the bottom block in length? That might be possible, but let's assume the diagram intends for us to calculate as given.

Perhaps the "10 m" is a typo? Or perhaps I'm misreading orientation.

Alternative approach: Maybe the 10 m is the depth, and 6 m is the length? But the diagram usually puts length along front.

I recall that in some diagrams, the dimension labeled on the top face might be depth.

Let me try this:

Assume for top block:
- Length (front to back) = 6 m
- Width (left to right) = 10 m
- Height = 3 m

For bottom block:
- Length = 6 m (same depth)
- Width = 9 m
- Height = 6 m

Then top block width 10 m > bottom block width 9 m — still overhang.

But mathematically, we can still compute.

Volume part 1: 10 × 6 × 3 = 180 m³

Volume part 2: 9 × 6 × 6 = 324 m³

Total = 180 + 324 = 504 m³

But is that correct? The problem might intend the blocks to be aligned without overhang, so perhaps the 10 m is a mistake, or perhaps it's the other way.

Wait — another possibility: the bottom block is 9 m wide, and the top block is sitting on it, but the top block's 10 m includes an extension? Unlikely.

Perhaps the 10 m is the length of the top block, and the bottom block is also 10 m, but labeled 9 m by mistake? But we have to go with what's given.

Let me look at part b, c, d for pattern.

Part b:
Dimensions:
One block: 8 m (length) × 6 m (width) × 7 m (height)? But there's a cutout.

Actually, part b is an L-shape.

From diagram:

There is a large block minus a small block, or two blocks added.

Typically, for b:

We can see:
- A vertical part: 5 m (width) × 6 m (depth) × 7 m (height)? But labeled 5 m, 6 m, 7 m, and also 3 m, 1 m, 8 m.

Better to interpret as:

The figure has:
- A back part: 8 m (length) × 6 m (width) × 7 m (height) — but no.

Standard way: Break into two rectangular prisms.

For part b:

Option 1:
- Left part: 5 m (width) × 6 m (depth) × 7 m (height) = 5×6×7 = 210
- Right part: but there's a notch.

Actually, from the labels:

The overall length is 8 m, but there's a step.

The bottom part has height 1 m, and the upper part has height 6 m (since 7-1=6), and width 5 m, and depth 6 m.

Also, the remaining part on the right: length = 8 - 5 = 3 m, width = 6 m, height = 1 m.

So two parts:

Part 1: the tall part: 5 m (w) × 6 m (d) × 6 m (h) = 5*6*6 = 180 m³? But height is from bottom to top of tall part, which is 7 m total, but the short part is 1 m high, so the tall part is 6 m above the short part? No.

Actually, the total height is 7 m. The short part is 1 m high, and the tall part is 7 m high, but they share the same base? No.

Better: the figure consists of:

- A base layer: 8 m (l) × 6 m (w) × 1 m (h) = 48 m³
- On top of the left part, a taller block: 5 m (l) × 6 m (w) × 6 m (h) = 180 m³ (since 7-1=6)

Total = 48 + 180 = 228 m³

Yes, that makes sense.

Similarly for others.

Back to part a.

For part a, likely:

The bottom block is 9 m (l) × 6 m (w) × 6 m (h) = 324 m³

The top block is 10 m (l) × 6 m (w) × 3 m (h) = 180 m³

Even though 10 > 9, perhaps it's intended, or perhaps the 10 m is depth.

Another idea: perhaps the 10 m is the depth for both, and the lengths are different.

In many diagrams, the dimension labeled on the side might be depth.

Assume that "6 m" is the depth for both blocks.

Then for top block: length = 10 m, depth = 6 m, height = 3 m → vol = 180

For bottom block: length = 9 m, depth = 6 m, height = 6 m → vol = 324

Total 504 m³

I think we have to go with that.

Perhaps the top block is centered or something, but volume is just sum.

So for a:

Volume of part 1: 10 × 6 × 3 = 180 m³

Volume of part 2: 9 × 6 × 6 = 324 m³

Volume of shape: 180 + 324 = 504 m³

Now part b:

As above:

We can split into:

- The lower slab: length 8 m, width 6 m, height 1 m → 8×6×1 = 48 m³

- The upper block on left: length 5 m, width 6 m, height 6 m (since total height 7 m, minus 1 m base) → 5×6×6 = 180 m³

Total = 48 + 180 = 228 m³

Some might do it as one big block minus a missing part, but this is fine.

Part c:

Diagram: looks like an L-shape standing up.

Labels: 2 cm, 11 cm, 8 cm, 3 cm, 4 cm, 5 cm.

Break into two parts.

Option:

- Vertical part: 2 cm (w) × 5 cm (d) × 11 cm (h) ? But there's a horizontal part.

From the diagram:

There is a tall thin part and a short wide part.

Specifically:

- Left part: width 2 cm, depth 5 cm, height 11 cm → vol = 2*5*11 = 110 cm³

- Right part: but it's attached at the bottom.

The right part has: length 4 cm (but wait, the total width at bottom is 5 cm? Labels say 4 cm and 5 cm.

Actually, from the diagram:

The base has width 5 cm (total), and the vertical part is 2 cm wide, so the horizontal part extending right is 5 - 2 = 3 cm? But labeled 4 cm? Confusing.

Look at labels:

On the front: left side has 2 cm (width of vertical part), then below it, the horizontal part has length 4 cm? And depth 5 cm? Also, height of horizontal part is 3 cm, and the vertical part goes up 11 cm, but the horizontal part is at the bottom, so the vertical part's height from base is 11 cm, but the horizontal part is 3 cm high, so they overlap in height? No.

Standard interpretation:

The figure has:

- A vertical rectangle: 2 cm (w) × 5 cm (d) × 11 cm (h) = 110 cm³

- A horizontal rectangle attached to its right at the bottom: this has length 4 cm (as labeled), width 5 cm (depth), height 3 cm.

But if the vertical part is 2 cm wide, and the horizontal part is 4 cm long, and they are adjacent, then total width would be 2 + 4 = 6 cm, but the diagram shows total width 5 cm? Contradiction.

Perhaps the 4 cm is the length of the horizontal part, and it starts from the left, but the vertical part is on top of it or something.

Another way: perhaps the horizontal part is under the vertical part.

Let me read the labels carefully.

In part c:

- The leftmost dimension is 2 cm (width of the tall part)

- Below that, the horizontal part has a length of 4 cm (from left to right)

- The depth is 5 cm for both? Labeled 5 cm on the side.

- The height of the horizontal part is 3 cm

- The total height of the tall part is 11 cm, which includes the 3 cm of the horizontal part? Or not?

Typically, in such diagrams, the 11 cm is the full height of the vertical part, and the horizontal part is separate at the bottom.

But if the horizontal part is 3 cm high, and the vertical part is 11 cm high, and they are stacked, then the vertical part would be on top of the horizontal part, but then the width might not match.

Assume that the horizontal part is at the bottom, spanning the full width.

From the diagram, the total width at the bottom is 5 cm (labeled).

The vertical part is 2 cm wide, so if it's on the left, then the horizontal part must extend to the right, but the horizontal part is labeled 4 cm long — which might be from the left edge.

Perhaps the horizontal part is 4 cm long and 5 cm deep, 3 cm high, and the vertical part is 2 cm wide, 5 cm deep, and 8 cm high (since 11 - 3 = 8), sitting on top of the left part of the horizontal part.

That makes sense.

So:

- Bottom horizontal part: length 4 cm, width 5 cm, height 3 cm → vol = 4*5*3 = 60 cm³

- Top vertical part: width 2 cm, depth 5 cm, height 8 cm (because total height 11 cm minus 3 cm of base) → vol = 2*5*8 = 80 cm³

Total = 60 + 80 = 140 cm³

Yes, that seems consistent.

If the vertical part were 11 cm high including the base, but then it would be overlapping, but volume would double-count, so better to have non-overlapping parts.

So I'll go with that.

Part d:

Diagram: looks like a large block with a smaller block attached or cut out.

Labels: 9 m, 10 m, 5 m, 12 m, 6 m, 2 m, 3 m.

From the diagram:

It seems like a main block and a protrusion.

Specifically:

- Main block: length 12 m, width 5 m, height ?

Total height is 9 m? Labeled on left.

Also, there is a part that is higher: 10 m? No, 10 m is probably length.

Let's see:

The front view: left side height 9 m, right side has a step.

There is a dimension 6 m and 3 m on the right.

Probably, the figure has:

- A large block: 12 m (l) × 5 m (w) × 6 m (h) ? But total height is 9 m.

Actually, from the diagram:

The main body has height 6 m, and on top of the right part, there is an additional block of height 3 m (since 9-6=3), and length 3 m? Labeled 3 m.

Also, the depth is 5 m for all? Labeled 5 m on the side.

And the length: total length 12 m, but the raised part is only on part of it.

Specifically, the raised part has length 3 m (as labeled), and the rest is lower.

So:

- Lower part: length 12 m, width 5 m, height 6 m → vol = 12*5*6 = 360 m³

- Upper part: on the right, length 3 m, width 5 m, height 3 m (since 9-6=3) → vol = 3*5*3 = 45 m³

Total = 360 + 45 = 405 m³

But is the upper part only 3 m long? The diagram shows "3 m" on the right side, probably indicating the length of the raised section.

Also, there is "6 m" labeled, which might be the length of the lower part before the raise, but total is 12 m, so if raised part is 3 m, then the flat part is 9 m? But 9+3=12, yes.

In the diagram, it shows "9 m" on the top left, which might be the length of the main part, but let's see.

Actually, looking back: in part d, it says "9 m" on the top left edge, "10 m" on the top right? No.

The user's image description: for d, it has "9 m", "10 m", "5 m", "12 m", "6 m", "2 m", "3 m".

Perhaps "10 m" is a typo or for another part.

In the initial problem statement, for d: "9 m", "10 m", etc., but in context, likely:

From standard problems, often:

The main block is 12 m long, 5 m wide, 6 m high.

Then on the right end, there is a block that is 3 m long (along length), 5 m wide, and 3 m high (additional height).

So volume as above.

To confirm, total height is 9 m, so the added height is 3 m.

Length of added part: labeled 3 m.

Depth: 5 m.

So vol upper = 3 * 5 * 3 = 45

Vol lower = 12 * 5 * 6 = 360

Total 405

But is the lower part really 12 m long including where the upper part is? Yes, because the upper part is on top, so the lower part is full 12 m.

Yes.

Some might think the lower part is only 9 m, but the diagram shows "12 m" as total length.

In the label, "12 m" is on the bottom front, so total length is 12 m.

"9 m" might be the length of the left part, but since the upper part is on the right, and labeled 3 m, then 9 + 3 = 12, so the lower part is continuous.

So yes.

Now, to summarize:

Part a:

Part 1: 10 × 6 × 3 = 180 m³

Part 2: 9 × 6 × 6 = 324 m³

Total: 180 + 324 = 504 m³

Part b:

Part 1 (base): 8 × 6 × 1 = 48 m³

Part 2 (tall left): 5 × 6 × 6 = 180 m³ (height 6 m because 7-1)

Total: 48 + 180 = 228 m³

Part c:

Part 1 (bottom horizontal): 4 × 5 × 3 = 60 cm³

Part 2 (top vertical): 2 × 5 × 8 = 80 cm³ (height 8 m because 11-3)

Total: 60 + 80 = 140 cm³

Part d:

Part 1 (lower block): 12 × 5 × 6 = 360 m³

Part 2 (upper block): 3 × 5 × 3 = 45 m³

Total: 360 + 45 = 405 m³

Now, for the answer format, since ExplainAnswer is false, TeachTopic is false, GeneratePractice is false, we only provide Final Answer.

But the problem asks to fill in the blanks for each part.

For part a, it has:

Volume of part 1: ___ x ___ x ___ = ___ m³

Volume of part 2: ___ x ___ x ___ = ___ m³

Volume of shape: ___ + ___ = ___ m³

Similarly for others, but for b,c,d, it just has lines, so probably we need to provide the volumes.

Since the instruction is to solve the problem, and final answer should be the completed values.

But in the response, since no explanation is to be shown, we just give the final numerical answers for each part.

However, the Final Answer section should contain the complete solution as per the worksheet.

Perhaps list the volumes for each part.

Since it's multiple parts, we can state:

For a: part1=180, part2=324, total=504

For b: total=228

For c: total=140

For d: total=405

But to match the worksheet, for a, we need to specify the multiplications.

In the Final Answer, we can write the filled-in values.

Given the constraints, I'll provide the final volumes for each composite figure, and for a, the breakdown.

But the instruction says: "Final Answer: [Provide only the final correct answer]"

And since it's a worksheet with blanks, perhaps list the answers as per the blanks.

To be safe, I'll provide the total volumes for each part, as that's what is ultimately asked ("find the volume of each solid figure").

For part a, it explicitly asks for parts, so we should include that.

In the response, since no explanation, just the numbers.

I think for Final Answer, we can write:

a. Volume of part 1: 10 × 6 × 3 = 180 m³
Volume of part 2: 9 × 6 × 6 = 324 m³
Volume of shape: 180 + 324 = 504 m³

b. 228 m³
c. 140 cm³
d. 405 m³

But units are different, so keep as is.

Now, double-check calculations.

Part a:
10*6*3=180, correct
9*6*6=324, correct
180+324=504, correct

Part b:
Base: 8*6*1=48
Tall: 5*6*6=180 (height 6m, since total 7m minus 1m base)
48+180=228, correct

Part c:
Bottom: 4*5*3=60
Top: 2*5*8=80 (height 8cm, since 11-3=8)
60+80=140, correct

Part d:
Lower: 12*5*6=360
Upper: 3*5*3=45
360+45=405, correct

All good.

Final Answer:
a. Volume of part 1: 10 × 6 × 3 = 180 m³
Volume of part 2: 9 × 6 × 6 = 324 m³
Volume of shape: 180 + 324 = 504 m³
b. 228 m³
c. 140 cm³
d. 405 m³