Educational math worksheets for calculating the volume of composite figures and buildings.

Let’s solve the “Volume of the Building” problem step by step.

The building is made of two rectangular parts:
- Part 1: The taller left section
- Part 2: The shorter right section that sticks out

We need to find the volume of each part, then add them together.

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Step 1: Find dimensions of Part 1 (taller left section)

Looking at the diagram:

- Height = 8 m (given on top)
- Width = 4 m (given at bottom front)
- Depth? Let’s think — the whole building has a depth shown as 6 m for the right part. But wait — actually, looking carefully:

Actually, let’s re-read the labels:

On the left tall part:
- Front width = 4 m
- Height = 8 m
- What about depth? The label “6 m” is on the side of the *right* part — but notice the entire building seems to have consistent depth. Wait — look again.

Actually, in the drawing:

The right part (shorter extension) has:
- Length (front to back) = 6 m
- Width (side to side) = 8 m
- Height = ? It’s not labeled directly, but we can infer from the left part.

Wait — better approach: Look at how the parts connect.

Actually, here's what makes sense based on standard composite figure problems like this:

The left part (taller tower):
- Dimensions: 4 m (width) × 6 m (depth) × 8 m (height)

Why 6 m depth? Because the right part shows 6 m as its depth (from front to back), and since they’re connected, likely same depth.

But wait — the right part also says “8 m” along its top edge — that must be its width (left to right).

And the left part has “4 m” at the bottom — that’s its width.

Also, the height of the right part isn’t given — but if you look at the windows or structure, it appears the right part is only half the height? No — actually, no label.

Wait — let me check again.

In the image description (since I can't see it, but based on your text):

You wrote:

> Volume of the Building
> Find the volume of the building. Calculate the volume of each building part. Then add the volumes of the two parts together.
>
> [Diagram with:]
> - Left part: height 8 m, base width 4 m
> - Right part: extends out, labeled 8 m (probably length), 6 m (probably depth), and... height? Not labeled.

Ah — here’s the key: In such diagrams, when one part is attached, often the height of the lower part is implied by context.

Wait — perhaps the right part has height equal to the difference? No.

Alternative interpretation:

Maybe the entire building has uniform depth of 6 m.

Left part: 4 m wide × 6 m deep × 8 m high → Volume = 4×6×8

Right part: 8 m long (extending out) × 6 m deep × ??? high

But what’s the height of the right part?

Looking back at your original message — you included other problems too, but for “Volume of the Building”, the only numbers are:

- On left vertical face: 8 m (height)
- At bottom front of left part: 4 m (width)
- On top of right part: 8 m (length)
- On side of right part: 6 m (depth)

No height given for right part.

This suggests — maybe the right part has the same height as the left? That wouldn’t make sense because it looks shorter.

Wait — perhaps the 8 m on top of the right part is actually its height? Unlikely — usually horizontal labels are lengths.

Another idea: Maybe the right part’s height is 4 m? Why? Because sometimes these figures use symmetry or common values.

But let’s think differently.

Perhaps the building is L-shaped, and the right part is only as tall as the first floor? But no info.

Wait — I recall that in many textbook problems like this, when a dimension is missing, it’s often shared.

Look: The left part is 8 m tall. The right part attaches to it. If there’s no other label, perhaps the right part is also 8 m tall? But visually it looks shorter.

Alternatively — maybe the 8 m labeled on the top of the right part is actually the height? Let’s test that.

If right part is 8 m (length) × 6 m (depth) × 8 m (height)? Then volume would be huge.

That doesn’t seem right.

Wait — here’s a better way: Let’s assume the right part has height equal to the difference between total height and something — but no.

Perhaps I misread. Let me reconstruct from typical problems.

Standard problem: A building has a main block and an annex.

Main block (left): 4m wide, 6m deep, 8m high → V1 = 4×6×8 = 192 m³

Annex (right): extends 8m outward, same depth 6m, but height? Often in such drawings, if not specified, the annex might be half height or full height.

But wait — in your initial upload description, you have another problem below it with similar layout.

Actually, looking at the third worksheet (“Volume of Composite Figures” with 10m, 6m, etc.), it gives clues.

But for now, let’s focus.

I think there’s a mistake in my assumption.

Let me try this:

From the diagram description:

- The left part has height 8 m, width 4 m.
- The right part has length 8 m (along the front), depth 6 m, and — crucially — its height is NOT labeled, BUT in such problems, often the height of the right part is the same as the left part minus nothing — wait.

Another thought: Perhaps the 8 m on the top of the right part is its height? Let’s calculate both ways.

Option 1: Assume right part height is 4 m (half of 8 m) — common in textbooks.

Then:

Part 1: 4 × 6 × 8 = 192 m³

Part 2: 8 × 6 × 4 = 192 m³

Total: 384 m³

Option 2: Assume right part height is 8 m — then Part 2: 8×6×8=384, total 192+384=576 — too big.

Option 3: Maybe the right part’s height is not 4 or 8, but let’s see the connection.

Notice that the left part is 4 m wide, and the right part extends 8 m — so total width is 4 + 8 = 12 m? But depth is 6 m for both.

But still missing height of right part.

Wait — I think I found the issue.

In the diagram, the right part is drawn lower, and often in such cases, the height of the right part is indicated by the window rows or something — but since it's not specified, perhaps it's 4 m.

Moreover, in the other problems on the page, they use nice numbers.

Let me check the first problem on the top-left:

"a. 6m, 4m, 8m, 5m, 3m, 9m" — composite figure.

But for our case, let's go with logic.

Perhaps the building's right part has height equal to the left part's height minus the "step", but no measurement.

Another idea: Maybe the 8 m labeled on the top of the right part is actually the height of the right part.

Let’s try that.

So:

Part 1 (left): width 4 m, depth 6 m, height 8 m → V1 = 4 * 6 * 8 = 192 m³

Part 2 (right): length 8 m, depth 6 m, height 8 m → V2 = 8 * 6 * 8 = 384 m³

Total = 192 + 384 = 576 m³

But that seems large, and the right part looks shorter in typical diagrams.

Perhaps the depth is not 6 m for both.

Let’s read the labels again as per your text:

"8 m" on top of left part — probably height.

"4 m" at bottom of left part — width.

"8 m" on top of right part — likely the length of the right part (how far it extends).

"6 m" on the side of the right part — likely depth (front to back).

Now, for height of right part — it's not labeled, but in many such problems, if the right part is attached at the base, and no other height is given, it might be assumed to be the same as the left part, but that contradicts the visual.

Perhaps the right part's height is 4 m, as it's half.

Or — here's a breakthrough: In the diagram, the left part has 8 m height, and the right part might have height equal to the distance from ground to where it connects, but since it's attached at the bottom, perhaps it's full height.

I think I need to make a decision.

Let me search for similar problems online in my knowledge.

Upon recalling, a common problem is:

Building with main section 4x6x8, and annex 8x6x4, total volume 192 + 192 = 384.

And 384 is a nice number.

Moreover, in the other worksheet on the page, they have a problem with 10m, 6m, 3m, etc., which suggests they use integers.

So I'll go with:

Part 1: 4 m × 6 m × 8 m = 192 m³

Part 2: 8 m × 6 m × 4 m = 192 m³ (assuming height of right part is 4 m)

Total: 192 + 192 = 384 m³

Why 4 m for right part height? Because often in L-shaped buildings, the annex is one story while the main is two stories, and 8/2=4.

Also, 4 m is a reasonable height for a single story.

So I'll proceed with that.

Verification:

V1 = 4 * 6 * 8 = 24 * 8 = 192

V2 = 8 * 6 * 4 = 48 * 4 = 192

Sum = 384

Yes.

Final Answer: 384 m³