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

Let's solve each problem step by step to find the volume of the given 3D shapes (cuboids or combinations of cuboids). The volume of a cuboid is calculated using:

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

We'll break complex shapes into simpler cuboids, calculate their volumes separately, and then add or subtract as needed.

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1)

This shape consists of two cuboids:

- Bottom part:
Length = 4 cm, Width = 2 cm, Height = 2 cm
Volume = $ 4 \times 2 \times 2 = 16 \, \text{cm}^3 $

- Top part:
Length = 2 cm, Width = 2 cm, Height = 2 cm
Volume = $ 2 \times 2 \times 2 = 8 \, \text{cm}^3 $

> Total Volume = $ 16 + 8 = \boxed{24} \, \text{cm}^3 $

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2)

This shape has two parts:

- Left part:
Length = 5 cm, Width = 2 cm, Height = 6 cm
Volume = $ 5 \times 2 \times 6 = 60 \, \text{cm}^3 $

- Right part (top):
Length = 4 cm, Width = 2 cm, Height = 6 cm
But wait — it's only on top, so height is 4 cm? Let’s clarify.

Actually, looking at the figure:
- The base is 6 cm long and 2 cm high.
- The left block is 5 cm wide, 6 cm long, 2 cm high.
- The right block is 4 cm wide, 6 cm long, but only 4 cm high?

Wait — no. The total depth is 6 cm. The front face shows:
- Left section: 5 cm tall → height = 5 cm?
But the label says "5 cm" on the side.

Wait — let's interpret carefully.

Looking again:

- The bottom base is 6 cm (length), 6 cm (depth), and 2 cm (height) — but wait, the depth is 2 cm (from side view).
- Actually, the depth is 2 cm (as labeled on the right side).

So:
- The entire shape has depth = 2 cm (into page), length = 6 cm (front-back), height varies.

But the figure shows:

- A large rectangular block:
- Length = 6 cm, Depth = 2 cm, Height = 5 cm → Volume = $ 6 \times 2 \times 5 = 60 \, \text{cm}^3 $
- Then a smaller block on top of the right side:
- It extends 4 cm in height above the base? Wait, the height of the small block is 4 cm, but the base is already 5 cm?

Wait — this seems inconsistent.

Let’s re-analyze:

The total height is 5 cm (left side), and the right side has a step down of 4 cm.

So:
- The left block:
- Length = 6 cm, Depth = 2 cm, Height = 5 cm → $ 6 \times 2 \times 5 = 60 \, \text{cm}^3 $

- The right block:
- It's lower, height = 4 cm? But it's not attached properly.

Wait — actually, the shape has a notch.

Better approach: Think of it as a big cuboid minus a smaller one.

- Big cuboid:
- Length = 6 cm, Width = 6 cm, Height = 5 cm? No — depth is 2 cm.

Wait — dimensions:

From labels:
- Front depth = 2 cm (right side)
- Length (along base) = 6 cm
- Height on left = 5 cm
- Height on right = 4 cm? But there’s a 4 cm label on the top.

Actually, look at the top view: The top surface is missing a piece.

Wait — better: This shape is made of two parts.

Let’s split:

- Lower block:
- Covers entire base: length = 6 cm, depth = 2 cm, height = 4 cm → Volume = $ 6 \times 2 \times 4 = 48 \, \text{cm}^3 $

- Upper block:
- On the left side, adds extra height:
- Length = 6 cm, depth = 2 cm, height = 1 cm (since 5 cm total height, 4 cm base → extra 1 cm)
→ Volume = $ 6 \times 2 \times 1 = 12 \, \text{cm}^3 $

Wait — but the label says "5 cm" on the left side, and "4 cm" on the top.

So yes:
- Base: 6 cm × 2 cm × 4 cm = 48 cm³
- Top layer: 6 cm × 2 cm × 1 cm = 12 cm³
→ Total = $ 48 + 12 = \boxed{60} \, \text{cm}^3 $

Alternatively, think of it as:
- Whole block: 6×2×5 = 60 cm³
- But the right part is only 4 cm high? No — the whole height is 5 cm on the left, but the right side is shorter?

Wait — the diagram shows a step, like an L-shape.

Wait — the top has a 4 cm label, and the side has a 5 cm label.

Let me draw mentally:

- The shape has:
- A base of 6 cm (length), 2 cm (depth), 4 cm (height) → Volume = 48 cm³
- A top extension on the left: 6 cm (length), 2 cm (depth), 1 cm (height) → 12 cm³
→ Total = 60 cm³

Yes.

✔ Answer: $ \boxed{60} \, \text{cm}^3 $

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3)

This is a stepped shape with three levels.

Break into three cuboids:

- Bottom layer:
- Length = 5 cm, Width = 3 cm, Height = 2 cm
→ Volume = $ 5 \times 3 \times 2 = 30 \, \text{cm}^3 $

- Middle layer:
- Length = 3 cm, Width = 3 cm, Height = 2 cm
→ Volume = $ 3 \times 3 \times 2 = 18 \, \text{cm}^3 $

- Top layer:
- Length = 3 cm, Width = 3 cm, Height = 2 cm
→ Volume = $ 3 \times 3 \times 2 = 18 \, \text{cm}^3 $

Wait — but the middle and top are stacked?

Actually, from the diagram:

- Bottom: full width = 5 cm, depth = 3 cm, height = 2 cm → 30 cm³
- Middle: sits on top of bottom, centered? But width = 3 cm, so it's inset.
- So: 3 cm (length), 3 cm (depth), 2 cm (height) → 18 cm³
- Top: same size as middle? Yes, 3×3×2 = 18 cm³

But wait — the top layer is on top of the middle, so total height is 6 cm?

But the labels show:
- Height of bottom = 2 cm
- Middle = 2 cm
- Top = 2 cm → total 6 cm

So all good.

Total volume = $ 30 + 18 + 18 = \boxed{66} \, \text{cm}^3 $

✔ Answer: $ \boxed{66} \, \text{cm}^3 $

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4)

This is a zig-zag shape.

Split into three cuboids:

- Left block:
- Length = 3 cm, Depth = 4 cm, Height = 2 cm → $ 3 \times 4 \times 2 = 24 \, \text{cm}^3 $

- Middle block:
- Length = 4 cm, Depth = 4 cm, Height = 2 cm → $ 4 \times 4 \times 2 = 32 \, \text{cm}^3 $? Wait — depth is 4 cm, but the block is only 4 cm long?

Wait — labels:
- Depth = 4 cm (on right side)
- Height = 2 cm (bottom)
- Top block: 1 cm high, 2 cm long, 4 cm deep

Let’s analyze:

- The bottom layer:
- Full length = 3 cm + 4 cm = 7 cm? No — looks like a step.

Actually, from the side:
- The base is 4 cm deep (into page)
- The shape has:
- A left step: 3 cm wide, 2 cm high
- A middle step: 4 cm wide, 4 cm high? No — height is only 2 cm for base.

Wait — labels:
- Height of base = 2 cm
- Height of top block = 1 cm
- Depth = 4 cm
- Widths: 3 cm, 4 cm, 2 cm

Better to split:

1. Bottom block:
- Length = 3 cm, Depth = 4 cm, Height = 2 cm → $ 3 \times 4 \times 2 = 24 \, \text{cm}^3 $

2. Middle block:
- Length = 4 cm, Depth = 4 cm, Height = 2 cm → $ 4 \times 4 \times 2 = 32 \, \text{cm}^3 $

3. Top block:
- Length = 2 cm, Depth = 4 cm, Height = 1 cm → $ 2 \times 4 \times 1 = 8 \, \text{cm}^3 $

Wait — but are these aligned?

From the diagram:
- The bottom is 3 cm wide (left), then 4 cm wide (middle), total 7 cm? But the label says "3 cm" and "4 cm" — so maybe:
- Left: 3 cm wide, 2 cm high
- Middle: 4 cm wide, 2 cm high
- Top: 2 cm wide, 1 cm high, sitting on the middle?

But the top block is only 2 cm long and 1 cm high, placed on the right side.

Wait — actually, the top block is 2 cm long, 1 cm high, 4 cm deep — so it sits on top of the right end.

But the middle block is 4 cm wide, so the top block can sit on it.

But the bottom block is only 3 cm wide, so the rest is supported by the middle?

No — the structure is:

- Bottom layer:
- A base of 3 cm (left) + 4 cm (right) = 7 cm long? But the diagram shows a gap.

Wait — perhaps it's:

- Left block: 3 cm × 4 cm × 2 cm → 24 cm³
- Right block: 4 cm × 4 cm × 2 cm → 32 cm³
- Top block: 2 cm × 4 cm × 1 cm → 8 cm³

But do they overlap? No — the left and right are adjacent.

But the top block is on top of the right block.

So total volume = $ 24 + 32 + 8 = \boxed{64} \, \text{cm}^3 $

But wait — is the right block really 4 cm wide? The label says "4 cm" on the bottom, but the total length is 3 cm + 4 cm = 7 cm?

Yes — so total length = 7 cm.

So:
- Left: 3×4×2 = 24
- Right: 4×4×2 = 32
- Top: 2×4×1 = 8
- Total = 24 + 32 + 8 = 64 cm³

✔ Answer: $ \boxed{64} \, \text{cm}^3 $

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5)

This is an L-shaped prism.

Split into two cuboids:

- Vertical arm:
- Length = 5 cm, Depth = 2 cm, Height = 5 cm → $ 5 \times 2 \times 5 = 50 \, \text{cm}^3 $

- Horizontal arm:
- Length = 7 cm, Depth = 1 cm, Height = 3 cm → $ 7 \times 1 \times 3 = 21 \, \text{cm}^3 $

Wait — but they share a common part? Look at the diagram:

- The vertical arm is 5 cm high, 5 cm long, 2 cm deep
- The horizontal arm is 7 cm long, 1 cm deep, 3 cm high
- They meet at a corner — but the overlap is a 5 cm × 1 cm × 3 cm block?

Wait — no — the horizontal arm is 3 cm high, and the vertical arm is 5 cm high, so the horizontal arm rests on the bottom of the vertical arm.

But the depth of the horizontal arm is 1 cm, while the vertical arm is 2 cm deep — so they don’t fully overlap.

Let’s read labels:

- Vertical arm:
- Length = 5 cm, Depth = 2 cm, Height = 5 cm → Volume = $ 5 \times 2 \times 5 = 50 \, \text{cm}^3 $

- Horizontal arm:
- Length = 7 cm, Depth = 1 cm, Height = 3 cm → $ 7 \times 1 \times 3 = 21 \, \text{cm}^3 $

But they intersect at a region: 5 cm (length) × 1 cm (depth) × 3 cm (height)

Wait — the horizontal arm is 7 cm long, but only overlaps 5 cm with the vertical arm?

Actually, the horizontal arm starts at the bottom of the vertical arm and extends 7 cm.

But the vertical arm is 5 cm long and 2 cm deep.

The horizontal arm is 1 cm deep, so it sits beside the vertical arm.

But the diagram shows a shared edge.

Wait — the horizontal arm is 7 cm long, 1 cm deep, 3 cm high — but it connects to the vertical arm.

But the vertical arm is 5 cm long, 2 cm deep, 5 cm high.

They intersect in a 5 cm × 1 cm × 3 cm block?

But that would be double-counting.

But actually, the horizontal arm is attached to the side of the vertical arm.

So no overlap — just touching.

So total volume = $ 50 + 21 = \boxed{71} \, \text{cm}^3 $

But wait — the horizontal arm is only 3 cm high, and the vertical arm is 5 cm high — so they don't interfere.

Yes — the horizontal arm is in front of the vertical arm, but only 1 cm deep, while vertical is 2 cm deep.

So no overlap.

✔ Answer: $ \boxed{71} \, \text{cm}^3 $

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6)

This is a large cuboid with a hole.

- Outer cuboid:
- Length = 8 cm, Width = 4 cm, Height = 6 cm
→ Volume = $ 8 \times 4 \times 6 = 192 \, \text{cm}^3 $

- Hole inside:
- The hole is a rectangular prism, dimensions:
- From diagram:
- The inner rectangle is 4 cm wide, 2 cm high, and depth = 4 cm?
- But the hole is shown as a square cutout.

Wait — the hole is not a full-through? It's a rectangular cavity.

From the diagram:
- The hole has:
- Length = 4 cm (top), Width = 2 cm (side), Height = 4 cm? No — the depth is 4 cm?

Wait — the hole is visible on the front face:
- It's 4 cm wide, 2 cm high, and since it's a cavity, its depth is equal to the width of the object? No — the object is 4 cm thick (into page).

Wait — the object is 8 cm (length), 4 cm (height), 6 cm (depth)? No — the depth is 4 cm? Wait:

Labels:
- Top: 8 cm
- Side: 6 cm
- Depth: 4 cm

So outer box: $ 8 \times 6 \times 4 = 192 \, \text{cm}^3 $

Now the hole:
- On the front face: a rectangle of 4 cm (width) × 2 cm (height)
- Since it's a cavity going through, its depth is the thickness of the object — which is 4 cm (into page)

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

Wait — but the hole is not going all the way through? The diagram shows a cavity that is not fully open.

Wait — the hole is shown as a square with a diagonal line — suggesting it's a rectangular prism cut out.

But the depth of the cavity is 4 cm (same as the thickness of the wall)?

Wait — the object has depth = 4 cm (into page), so the hole goes through the entire depth.

So yes:
- Hole: length = 4 cm, width = 2 cm, depth = 4 cm → Volume = $ 4 \times 2 \times 4 = 32 \, \text{cm}^3 $

But wait — the label says "4 cm" and "2 cm" — so it's 4 cm wide, 2 cm high.

And the depth is the same as the object’s depth: 4 cm.

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

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

But wait — is the hole fully enclosed? Or does it go through?

The diagram shows a cavity on the front face — but not necessarily through.

Wait — the inner rectangle is drawn with dashed lines — suggesting it's a cutout.

But the depth of the hole is not labeled.

However, the object’s depth is 4 cm, and the hole is drawn as a rectangle on the front — so likely it's a through-hole.

But the dimensions:
- The hole is 4 cm wide, 2 cm high — and since the object is 4 cm thick, the hole goes through.

So volume removed = $ 4 \times 2 \times 4 = 32 \, \text{cm}^3 $

So final volume = $ 8 \times 6 \times 4 = 192 $, minus $ 32 = \boxed{160} \, \text{cm}^3 $

But wait — the height of the object is 6 cm, and the hole is only 2 cm high — so yes.

✔ Answer: $ \boxed{160} \, \text{cm}^3 $

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✔ Final Answers:

1) $ \boxed{24} \, \text{cm}^3 $
2) $ \boxed{60} \, \text{cm}^3 $
3) $ \boxed{66} \, \text{cm}^3 $
4) $ \boxed{64} \, \text{cm}^3 $
5) $ \boxed{71} \, \text{cm}^3 $
6) $ \boxed{160} \, \text{cm}^3 $

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