Volume and surface area worksheet for calculating the volume of irregular cuboids, featuring six 3D shapes with labeled dimensions.

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 will 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 = 6 cm, Width = 2 cm, Height = 5 cm
Volume = $ 6 \times 2 \times 5 = 60 \, \text{cm}^3 $

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

> Total Volume = $ 60 + 16 = \boxed{76} \, \text{cm}^3 $

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3)

This shape has three cuboids:

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

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

- Right side block:
Length = 2 cm, Width = 3 cm, Height = 2 cm
Volume = $ 2 \times 3 \times 2 = 12 \, \text{cm}^3 $

> Total Volume = $ 30 + 18 + 12 = \boxed{60} \, \text{cm}^3 $

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4)

This shape has two parts:

- Bottom base:
Length = 3 cm, Width = 4 cm, Height = 2 cm
Volume = $ 3 \times 4 \times 2 = 24 \, \text{cm}^3 $

- Top part:
Length = 2 cm, Width = 4 cm, Height = 1 cm
Volume = $ 2 \times 4 \times 1 = 8 \, \text{cm}^3 $

> Total Volume = $ 24 + 8 = \boxed{32} \, \text{cm}^3 $

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5)

This shape looks like an "L" shape made of two cuboids:

- Vertical part (left):
Length = 5 cm, Width = 2 cm, Height = 5 cm
Volume = $ 5 \times 2 \times 5 = 50 \, \text{cm}^3 $

- Horizontal part (right):
Length = 7 cm, Width = 1 cm, Height = 3 cm
Volume = $ 7 \times 1 \times 3 = 21 \, \text{cm}^3 $

> But wait — there's an overlap! The horizontal part extends under the vertical one. However, from the diagram, the shared part is only 1 cm in width and 3 cm in height, and it overlaps for 2 cm in length?

Wait — let’s analyze carefully.

Looking at the figure:
- The vertical cuboid is: $ 5 \times 2 \times 5 = 50 $
- The horizontal cuboid is: $ 7 \times 1 \times 3 = 21 $
- But they share a common region of size: $ 2 \times 1 \times 3 = 6 \, \text{cm}^3 $? Wait — actually, no overlap in volume because the horizontal piece is only 1 cm wide and the vertical is 2 cm wide, so the horizontal sits beside it?

But looking closely: the horizontal part starts at the bottom and goes back 7 cm, but its height is 3 cm, while the vertical part is 5 cm high. So the horizontal part is attached to the bottom of the vertical one, but not overlapping in space.

Wait — actually, both are connected at the base, and the horizontal part extends forward.

But the bottom of the vertical part is 2 cm wide, and the horizontal part is 1 cm wide — so they don't overlap in space.

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

Wait — check dimensions again:

- Vertical cuboid:
Length = 5 cm (along front-back), Width = 2 cm (side), Height = 5 cm → $ 5 \times 2 \times 5 = 50 $

- Horizontal cuboid:
Length = 7 cm (front-back), Width = 1 cm (side), Height = 3 cm → $ 7 \times 1 \times 3 = 21 $

But the horizontal part connects to the bottom of the vertical one, and since the vertical is 5 cm tall, and horizontal is only 3 cm tall, and the horizontal part is 1 cm wide, and vertical is 2 cm wide, so no overlap.

Also, the horizontal part extends beyond the vertical one — so yes, no overlapping volume.

> Total Volume = $ 50 + 21 = \boxed{71} \, \text{cm}^3 $

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6)

This is a large cuboid with a hole cut out.

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

- Inner hole:
From the diagram, the hole is a rectangular prism inside, with:
- Length = 4 cm, Width = 2 cm, Height = 4 cm? Wait — the depth is not clearly shown.

Wait — the hole appears to be on the face, but we must interpret the cross-section.

Looking at the diagram: the cutout is on the front face, and it shows a rectangle of 4 cm × 2 cm, and the depth of the hole is not labeled.

But the height of the object is 4 cm, and the cutout is 4 cm tall — so likely the hole goes all the way through?

Wait — no: the cutout is only 2 cm deep, because the width of the object is 6 cm, and the cutout is 2 cm wide (from the side), but the depth is indicated as 2 cm.

Wait — label says "2 cm" next to the inner rectangle — that’s probably the depth of the hole.

Actually, looking at the drawing: the inner rectangle has:
- One side labeled 4 cm, another 2 cm
- And the depth (into the page) is implied to be 2 cm?

But the outer cuboid has width = 6 cm, and the cutout is 2 cm wide — so maybe the hole is 2 cm deep?

Wait — better interpretation: the hole is a rectangular prism that is 4 cm long, 2 cm wide, and 4 cm high? No — that would go through the whole height.

But the depth of the hole is 2 cm, because the width of the object is 6 cm, and the cutout is drawn with a 2 cm dimension pointing into the object.

Wait — the label "2 cm" is shown on the side of the cutout, which is depth.

So:

- Hole dimensions:
Length = 4 cm, Width = 2 cm, Depth = 2 cm
Volume = $ 4 \times 2 \times 2 = 16 \, \text{cm}^3 $

> Total Volume = Outer – Hole = $ 192 - 16 = \boxed{176} \, \text{cm}^3 $

But wait — is the hole through the entire height? Yes, because the height of the hole is 4 cm, same as the object.

And depth is 2 cm — meaning it goes 2 cm into the object.

So yes:
- Hole: $ 4 \, \text{cm (length)} \times 2 \, \text{cm (width)} \times 2 \, \text{cm (depth)} = 16 \, \text{cm}^3 $

So final volume: $ 192 - 16 = \boxed{176} \, \text{cm}^3 $

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✔ Final Answers:

1) $ \boxed{24} \, \text{cm}^3 $
2) $ \boxed{76} \, \text{cm}^3 $
3) $ \boxed{60} \, \text{cm}^3 $
4) $ \boxed{32} \, \text{cm}^3 $
5) $ \boxed{71} \, \text{cm}^3 $
6) $ \boxed{176} \, \text{cm}^3 $

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