Volume of 3D Shapes Worksheet | Fun and Engaging 8th Grade PDF ... - Free Printable

Let's solve each of the problems in Section A step by step, finding the volume of each 3D shape made up of cuboids (rectangular prisms). The formula for the volume of a cuboid is:

$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$

We'll break down each complex shape into simpler cuboids, calculate their volumes individually, and then sum them up.

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1)

This shape has two parts:
- Bottom part: A rectangular block with dimensions $4 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}$
- Top part: A smaller block on top, $2 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}$

But wait: looking closely:
- The bottom part is $4 \text{ cm}$ long, $2 \text{ cm}$ wide, and $2 \text{ cm}$ high.
- The top part sits on the right side, extending forward $2 \text{ cm}$, height $2 \text{ cm}$, depth $2 \text{ cm}$, but its length is only $2 \text{ cm}$, and it’s placed such that it adds height to the right half.

Actually, let's re-analyze:

The total base is $4 \text{ cm}$ long. The left portion is $2 \text{ cm}$ high, and the right portion is $4 \text{ cm}$ high. But both have the same width ($2 \text{ cm}$) and depth ($2 \text{ cm}$).

So we can split it into:
- Left block: $2 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}$ → Volume = $2 \times 2 \times 2 = 8 \text{ cm}^3$
- Right block: $2 \text{ cm} \times 2 \text{ cm} \times 4 \text{ cm}$ → Volume = $2 \times 2 \times 4 = 16 \text{ cm}^3$

Total volume = $8 + 16 = \boxed{24 \text{ cm}^3}$

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2)

This is an L-shaped prism.

We can split it into two rectangles:
- Front block: $6 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}$ → Volume = $6 \times 2 \times 2 = 24 \text{ cm}^3$
- Back block: $4 \text{ cm} \times 2 \text{ cm} \times 5 \text{ cm}$ → Wait, no — this is not correct.

Wait — better approach: look at the full shape.

It appears as a large rectangle missing a piece? Or better: think of it as two blocks.

From the drawing:
- The base is $6 \text{ cm}$ long, $2 \text{ cm}$ deep, and height varies.
- On the left, it's $5 \text{ cm}$ high, on the right, it's $2 \text{ cm}$ high.
- But there's a "step" in the middle.

Alternatively, divide it into:
- Lower block: spans entire length $6 \text{ cm}$, depth $2 \text{ cm}$, height $2 \text{ cm}$ → Volume = $6 \times 2 \times 2 = 24 \text{ cm}^3$
- Upper block: only on the left, $4 \text{ cm}$ long (since 6 - 2 = 4), depth $2 \text{ cm}$, height $3 \text{ cm}$ (because total height is 5, lower is 2, so upper is 3)

Wait — the total height on the left is 5 cm, and the lower part is 2 cm, so the upper part is $5 - 2 = 3 \text{ cm}$.

But the upper block extends from left to where?

Looking at the diagram:
- The upper block is $4 \text{ cm}$ long (from front to back?), no.

Actually, the horizontal dimension is labeled: the full base is $6 \text{ cm}$, and the vertical section on the left is $5 \text{ cm}$ tall, while the right side is $2 \text{ cm}$ tall.

But the depth is $2 \text{ cm}$ throughout.

So:
- The bottom layer: runs the full $6 \text{ cm}$ in length, $2 \text{ cm}$ in depth, $2 \text{ cm}$ in height → Volume = $6 \times 2 \times 2 = 24 \text{ cm}^3$
- The top layer: only on the left side, height $5 - 2 = 3 \text{ cm}$, length $4 \text{ cm}$ (since the overhang is $4 \text{ cm}$), depth $2 \text{ cm}$ → Volume = $4 \times 2 \times 3 = 24 \text{ cm}^3$

Wait — but the label says $4 \text{ cm}$ on the top edge — probably meaning the length of the upper block is $4 \text{ cm}$, and the lower block is $6 \text{ cm}$.

Yes, so:
- Lower block: $6 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm} = 24 \text{ cm}^3$
- Upper block: $4 \text{ cm} \times 2 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^3$ → because height difference is $5 - 2 = 3 \text{ cm}$

Wait — but the upper block has height of $3 \text{ cm}$? Let's check.

Total height on left is $5 \text{ cm}$, bottom is $2 \text{ cm}$, so yes, upper part is $3 \text{ cm}$.

But the depth is $2 \text{ cm}$, and the length is $4 \text{ cm}$.

So volume = $4 \times 2 \times 3 = 24 \text{ cm}^3$

Total volume = $24 + 24 = \boxed{48 \text{ cm}^3}$

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3)

This is a three-level stepped shape.

Dimensions:
- Depth: $3 \text{ cm}$ throughout
- Height: $2 \text{ cm}$ at base, then another $2 \text{ cm}$ on top
- Length: $5 \text{ cm}$

Break into:
- Base layer: $5 \text{ cm} \times 3 \text{ cm} \times 2 \text{ cm}$ → Volume = $5 \times 3 \times 2 = 30 \text{ cm}^3$
- Middle layer: Only covers the center $3 \text{ cm}$ length (since it's $3 \text{ cm}$ wide), height $2 \text{ cm}$, depth $3 \text{ cm}$ → Volume = $3 \times 3 \times 2 = 18 \text{ cm}^3$
- Top layer: Only $3 \text{ cm}$ long, $3 \text{ cm}$ deep, $2 \text{ cm}$ high → Volume = $3 \times 3 \times 2 = 18 \text{ cm}^3$

Wait — but the top layer is only $3 \text{ cm}$ long? Yes.

So total volume = $30 + 18 + 18 = \boxed{66 \text{ cm}^3}$

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4)

This is a Z-shaped or bent shape.

We can split it into three cuboids:

From the diagram:
- Depth: $4 \text{ cm}$ throughout
- Height: $2 \text{ cm}$ at bottom, $4 \text{ cm}$ in middle, $1 \text{ cm}$ on top
- Widths vary

Let’s analyze:

- Bottom block: $3 \text{ cm}$ long, $4 \text{ cm}$ deep, $2 \text{ cm}$ high → Volume = $3 \times 4 \times 2 = 24 \text{ cm}^3$
- Middle block: $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high? No — height is $4 \text{ cm}$, but it's stacked.

Wait — actually, the total height is $2 + 4 + 1 = 7 \text{ cm}$, but the blocks are connected.

Better to split horizontally.

Actually, the structure has:
- A bottom layer: $3 \text{ cm}$ long, $4 \text{ cm}$ deep, $2 \text{ cm}$ high → $3 \times 4 \times 2 = 24 \text{ cm}^3$
- A middle layer: $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high? No — height is only $4 \text{ cm}$, but it's on top of the bottom.

Wait — the middle section is $4 \text{ cm}$ high, and it's $4 \text{ cm}$ long (in the direction of the base), and $4 \text{ cm}$ deep? But the depth is $4 \text{ cm}$, yes.

But the middle block is $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high? That would be $64$, too big.

Wait — the labels:
- Bottom: $3 \text{ cm}$ (horizontal), $2 \text{ cm}$ (vertical)
- Middle: $4 \text{ cm}$ (vertical), $4 \text{ cm}$ (horizontal)
- Top: $2 \text{ cm}$ (horizontal), $1 \text{ cm}$ (vertical)

And depth is $4 \text{ cm}$ throughout.

So:
- Bottom block: $3 \text{ cm} \times 4 \text{ cm} \times 2 \text{ cm} = 24 \text{ cm}^3$
- Middle block: $4 \text{ cm} \times 4 \text{ cm} \times 4 \text{ cm} = 64 \text{ cm}^3$? But that can't be — the middle block is only $4 \text{ cm}$ high, but it must fit on top.

Wait — the middle block is $4 \text{ cm}$ long (horizontal), $4 \text{ cm}$ deep, and $4 \text{ cm}$ high? But the total height of the middle is $4 \text{ cm}$, but it's stacked on the $2 \text{ cm}$ base.

But the top block is $2 \text{ cm}$ long, $4 \text{ cm}$ deep, $1 \text{ cm}$ high → $2 \times 4 \times 1 = 8 \text{ cm}^3$

Now, the middle block: it’s $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high → $4 \times 4 \times 4 = 64$? That seems way too big.

Wait — perhaps the middle block is only $4 \text{ cm}$ in height, but its length is $4 \text{ cm}$, and depth $4 \text{ cm}$, but that would make it $64$, which is impossible.

Let’s re-express.

Looking at the shape:
- It's like a bent bar.
- The bottom is $3 \text{ cm}$ long, $4 \text{ cm}$ deep, $2 \text{ cm}$ high → $3 \times 4 \times 2 = 24$
- Then a middle section: $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high? But that would extend beyond.

Wait — the middle is $4 \text{ cm}$ high, and it’s $4 \text{ cm}$ long, but the depth is still $4 \text{ cm}$.

But the total height is $2 + 4 + 1 = 7 \text{ cm}$, and the middle block is $4 \text{ cm}$ high, sitting on top of the $2 \text{ cm}$ base.

But the length of the middle block is $4 \text{ cm}$, and the depth is $4 \text{ cm}$, so volume = $4 \times 4 \times 4 = 64$? No — that’s wrong.

Wait — the horizontal dimension of the middle block is $4 \text{ cm}$, but it's in the same direction as the bottom.

But the bottom is only $3 \text{ cm}$ long, and the middle is $4 \text{ cm}$ long — so it extends beyond.

But the depth is $4 \text{ cm}$, so the middle block is $4 \text{ cm}$ (length) × $4 \text{ cm}$ (depth) × $4 \text{ cm}$ (height)? But that’s $64$, and total volume would be huge.

Wait — no! The height of the middle block is $4 \text{ cm}$, but the depth is $4 \text{ cm}$, and length is $4 \text{ cm}$ — so yes, $4 \times 4 \times 4 = 64$. But that can’t be.

Wait — no, the depth is $4 \text{ cm}$, but the height is $4 \text{ cm}$, and length is $4 \text{ cm}$ — so it’s a cube of $4 \times 4 \times 4 = 64$. But that seems too big.

But let’s check the top block: $2 \text{ cm}$ long, $4 \text{ cm}$ deep, $1 \text{ cm}$ high → $2 \times 4 \times 1 = 8$

Bottom: $3 \times 4 \times 2 = 24$

Middle: $4 \times 4 \times 4 = 64$? That’s impossible.

Wait — perhaps the middle block is $4 \text{ cm}$ in height, but only $4 \text{ cm}$ in length, and $4 \text{ cm}$ in depth — but that would be a cube.

But the figure shows a Z-shape, so likely:
- Bottom: $3 \text{ cm}$ long, $4 \text{ cm}$ deep, $2 \text{ cm}$ high → $24$
- Middle: $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high? No — the height is $4 \text{ cm}$, but it's only the vertical part.

Wait — perhaps the middle block is $4 \text{ cm}$ in length, $4 \text{ cm}$ in depth, and $4 \text{ cm}$ in height — but that’s $64$, and the top is $8$, bottom $24$, total $96$ — possible?

But let’s try another approach.

Perhaps the middle block is $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high — but that’s a cube.

But the top block is $2 \text{ cm}$ long, $4 \text{ cm}$ deep, $1 \text{ cm}$ high — $8$

And the bottom is $3 \text{ cm}$ long, $4 \text{ cm}$ deep, $2 \text{ cm}$ high — $24$

But the middle block is $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high — $64$ — total $24 + 64 + 8 = 96$

But that seems excessive.

Wait — maybe the middle block is not $4 \text{ cm}$ in height, but the total height is $4 \text{ cm}$, but it’s only $4 \text{ cm}$ in length and $4 \text{ cm}$ in depth.

But the label says “4 cm” on the side — likely the height.

Alternatively, perhaps the depth is $4 \text{ cm}$, and the height of the middle block is $4 \text{ cm}$, and the length is $4 \text{ cm}$ — so $4 \times 4 \times 4 = 64$ — yes.

But let’s accept that.

So:
- Bottom: $3 \times 4 \times 2 = 24$
- Middle: $4 \times 4 \times 4 = 64$
- Top: $2 \times 4 \times 1 = 8$

Total = $24 + 64 + 8 = \boxed{96 \text{ cm}^3}$

But wait — the top block is only $2 \text{ cm}$ long, but the middle is $4 \text{ cm}$ long — so they don't align.

Actually, the middle block is $4 \text{ cm}$ long, $4 \text{ cm}$ deep, $4 \text{ cm}$ high — but it’s placed vertically, so it’s $4 \text{ cm}$ in height, $4 \text{ cm}$ in depth, and $4 \text{ cm}$ in length.

Then the top block is $2 \text{ cm}$ long, $4 \text{ cm}$ deep, $1 \text{ cm}$ high — placed on top of the middle block.

So yes, the total volume is $24 + 64 + 8 = \boxed{96 \text{ cm}^3}$

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5)

This is an L-shaped prism.

Split into two parts:
- Vertical part: $5 \text{ cm}$ high, $2 \text{ cm}$ wide, $5 \text{ cm}$ deep → Volume = $5 \times 2 \times 5 = 50 \text{ cm}^3$
- Horizontal part: $7 \text{ cm}$ long, $3 \text{ cm}$ wide, $1 \text{ cm}$ high → Volume = $7 \times 3 \times 1 = 21 \text{ cm}^3$

But they overlap at the corner.

The overlapping region is $5 \text{ cm}$ long, $2 \text{ cm}$ wide, $1 \text{ cm}$ high — but wait, the horizontal part has width $3 \text{ cm}$, but only $2 \text{ cm}$ overlaps with the vertical part.

Wait — the horizontal part is $3 \text{ cm}$ in the depth direction? Let’s see:

From the diagram:
- Vertical part: $5 \text{ cm}$ high, $2 \text{ cm}$ wide, $5 \text{ cm}$ deep
- Horizontal part: $7 \text{ cm}$ long, $3 \text{ cm}$ wide, $1 \text{ cm}$ high

But the horizontal part is attached to the bottom of the vertical part.

The overlap is $5 \text{ cm}$ (depth) × $2 \text{ cm}$ (width) × $1 \text{ cm}$ (height) — but since it's a solid, we should avoid double-counting.

But if we split:
- Vertical block: $5 \times 2 \times 5 = 50$
- Horizontal block: $7 \times 3 \times 1 = 21$

But they intersect in a $5 \times 2 \times 1$ region — but since it's solid, we should add them directly, as the overlap is included in both.

No — the vertical block includes the bottom $1 \text{ cm}$, and the horizontal block also includes it — so we’re double-counting.

So we need to subtract the overlap.

Overlap volume: $5 \text{ cm}$ (depth) × $2 \text{ cm}$ (width) × $1 \text{ cm}$ (height) = $10 \text{ cm}^3$

But wait — the horizontal block is $3 \text{ cm}$ wide, but only $2 \text{ cm}$ of it overlaps with the vertical block.

So overlap = $5 \times 2 \times 1 = 10 \text{ cm}^3$

So total volume = $50 + 21 - 10 = \boxed{61 \text{ cm}^3}$

But wait — is the horizontal block really $3 \text{ cm}$ wide? Looking at the diagram, the horizontal part extends $3 \text{ cm}$ in the depth direction, but the vertical part is $5 \text{ cm}$ deep.

But the horizontal part is only $5 \text{ cm}$ long in depth? No.

Label says: horizontal part is $7 \text{ cm}$ long (along the length), $3 \text{ cm}$ wide (depth), $1 \text{ cm}$ high.

Vertical part: $5 \text{ cm}$ high, $2 \text{ cm}$ wide (length), $5 \text{ cm}$ deep.

They connect at a $2 \text{ cm} \times 5 \text{ cm} \times 1 \text{ cm}$ region.

So yes, overlap = $2 \times 5 \times 1 = 10 \text{ cm}^3$

So total volume = $50 + 21 - 10 = \boxed{61 \text{ cm}^3}$

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6)

This is a large cuboid with a hole in it.

Outer dimensions: $8 \text{ cm} \times 6 \text{ cm} \times 4 \text{ cm}$ → Volume = $8 \times 6 \times 4 = 192 \text{ cm}^3$

Inner hole: From the diagram, the hole is $4 \text{ cm} \times 2 \text{ cm} \times 4 \text{ cm}$? Wait.

The hole is shown as a rectangle inside, with dimensions:
- Width: $4 \text{ cm}$
- Depth: $2 \text{ cm}$
- Height: $4 \text{ cm}$ (same as outer height)

But the hole is not through the entire depth — wait, the outer depth is $6 \text{ cm}$, and the hole is $4 \text{ cm}$ wide, $2 \text{ cm}$ deep, $4 \text{ cm}$ high.

But the hole is only $2 \text{ cm}$ deep, and $4 \text{ cm}$ wide, $4 \text{ cm}$ high.

So volume of hole = $4 \times 2 \times 4 = 32 \text{ cm}^3$

So total volume = $192 - 32 = \boxed{160 \text{ cm}^3}$

But wait — is the hole fully within? Yes.

So final answer: $\boxed{160 \text{ cm}^3}$

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✔ Final Answers:

1) $24 \text{ cm}^3$
2) $48 \text{ cm}^3$
3) $66 \text{ cm}^3$
4) $96 \text{ cm}^3$
5) $61 \text{ cm}^3$
6) $160 \text{ cm}^3$

Let me know if you'd like the surface area as well!