Volume and surface area worksheet featuring six cuboid shapes with labeled dimensions for calculating volume.

Let's solve each of these problems step by step. The task is to find the volume of each 3D shape made up of cuboids (rectangular prisms). We'll break each shape into simpler cuboids, calculate their individual volumes using the formula:

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

Then sum them up.

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1)

This shape has two parts:
- Bottom part: 4 cm (length) × 2 cm (width) × 2 cm (height)
- Top part: 2 cm (length) × 2 cm (width) × 2 cm (height)

But wait — looking closely:
- The bottom is 4 cm long, 2 cm wide, and 2 cm high.
- The top is on the right side: it’s 2 cm long, 2 cm wide, and 2 cm high? Wait — height is 4 cm total, but bottom is 2 cm, so top must be 2 cm tall?

Wait — let's re-analyze carefully.

From the diagram:
- The full height is 4 cm.
- The left side is only 2 cm high, so the top block is 2 cm high.
- So:
- Bottom block: 4 cm (L) × 2 cm (W) × 2 cm (H) → $4 \times 2 \times 2 = 16$ cm³
- Top block: 2 cm (L) × 2 cm (W) × 2 cm (H) → $2 \times 2 \times 2 = 8$ cm³

Wait — but the top block extends over the bottom? Let's see: the top block is 2 cm wide, 2 cm deep, and 2 cm high. But it sits on top of the bottom block, which is 2 cm high.

So yes:
- Bottom: 4×2×2 = 16 cm³
- Top: 2×2×2 = 8 cm³

But wait — the depth (width) is 2 cm for both.

So total volume = 16 + 8 = 24 cm³

✔ Answer: 24 cm³

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2)

This shape looks like a "step" or L-shape.

We can split it into two cuboids:

- Left block: 5 cm (height) × 6 cm (length) × 2 cm (depth) → but wait — the height is 5 cm, but the front face shows 4 cm on top and 2 cm on bottom? No.

Wait — look at dimensions:
- Overall length: 6 cm
- Depth: 2 cm
- Height: 5 cm
- But there's a cut-out on the top-right.

Actually, this is a solid with a notch.

But better: think of it as a big cuboid minus a small one?

Or add two parts.

Let’s divide it into two parts:

Option: Two cuboids

- Front lower block: 6 cm (L) × 2 cm (W) × 2 cm (H) → $6 \times 2 \times 2 = 24$ cm³
- Back upper block: 4 cm (L) × 2 cm (W) × 3 cm (H)? Wait — height from base to top is 5 cm, but the lower part is 2 cm, so upper is 3 cm?

Wait — no. From diagram:
- The height of the whole object is 5 cm.
- The front part is 2 cm high, the back part is 5 cm high.
- The width (depth) is 2 cm throughout.
- Length: 6 cm

But the notch is missing? Or is it solid?

Wait — actually, the figure is solid. It's like a staircase.

Better way: split into two rectangular blocks:

- Block A (bottom): 6 cm (L) × 2 cm (W) × 2 cm (H) → $6 \times 2 \times 2 = 24$
- Block B (top): 4 cm (L) × 2 cm (W) × 3 cm (H) → because height from 2 cm to 5 cm is 3 cm → $4 \times 2 \times 3 = 24$

Total volume = 24 + 24 = 48 cm³

✔ Answer: 48 cm³

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3)

This is a three-level step-like structure.

Break into 3 cuboids:

- Bottom layer: 5 cm (L) × 3 cm (W) × 2 cm (H) → $5 \times 3 \times 2 = 30$
- Middle layer: 3 cm (L) × 3 cm (W) × 2 cm (H) → $3 \times 3 \times 2 = 18$
- Top layer: 3 cm (L) × 3 cm (W) × 2 cm (H) → $3 \times 3 \times 2 = 18$

Wait — but middle and top are both 3 cm long? Yes, from the diagram.

But the top layer is only 3 cm long and 3 cm wide.

So total volume = 30 + 18 + 18 = 66 cm³

Wait — is that correct?

Let’s check:

- Bottom: full 5 cm long, 3 cm wide, 2 cm high → 30
- Middle: sits on top of bottom, but only 3 cm long (centered?), so 3×3×2 = 18
- Top: same size, 3×3×2 = 18

Yes, total = 30 + 18 + 18 = 66 cm³

✔ Answer: 66 cm³

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4)

This is an S-shaped or zigzag structure.

Break into 3 parts:

- Bottom block: 3 cm (L) × 4 cm (W) × 2 cm (H) → $3 \times 4 \times 2 = 24$
- Middle block: 2 cm (L) × 4 cm (W) × 1 cm (H) → $2 \times 4 \times 1 = 8$
- Top block: 4 cm (L) × 4 cm (W) × 1 cm (H) → $4 \times 4 \times 1 = 16$

Wait — but the depth is 4 cm? Let's see.

Looking at the diagram:

- The base is 3 cm long, 4 cm wide, 2 cm high → 3×4×2 = 24
- Then a middle horizontal section: 2 cm long, 4 cm wide, 1 cm high → 2×4×1 = 8
- Then a top section: 4 cm long, 4 cm wide, 1 cm high → 4×4×1 = 16

But does the top extend beyond the middle?

Yes — the total length is 3 + 2 + 4 = 9 cm? But labeled as 4 cm on the right.

Wait — maybe I misread.

Look at labels:

- Bottom: 3 cm (length), 4 cm (depth), 2 cm (height)
- Middle: 2 cm (length), 4 cm (depth), 1 cm (height)
- Top: 4 cm (length), 4 cm (depth), 1 cm (height)

But the total length is 3 + 2 + 4 = 9 cm? But the diagram shows 3 cm on the bottom, then 2 cm in middle, then 4 cm on top — but they are aligned.

Wait — actually, the total length is 3 + 2 + 4 = 9 cm? But the diagram shows only 3 cm on the bottom, and 4 cm on the right.

Wait — perhaps the depth is 4 cm, and length varies.

Wait — the horizontal dimension (left to right) is shown as 3 cm for bottom, then 2 cm for middle, then 4 cm for top.

But the depth (into page) is 4 cm? Wait — no.

Wait — the side view shows:
- Bottom: 3 cm (length), 2 cm (height)
- Middle: 2 cm (length), 1 cm (height)
- Top: 4 cm (length), 1 cm (height)

And depth is 4 cm? But labeled on the side as 4 cm.

Wait — the label says "4 cm" next to the depth — so depth = 4 cm.

So all blocks have depth = 4 cm

So:
- Bottom block: 3 cm (L) × 4 cm (W) × 2 cm (H) → $3 \times 4 \times 2 = 24$
- Middle block: 2 cm (L) × 4 cm (W) × 1 cm (H) → $2 \times 4 \times 1 = 8$
- Top block: 4 cm (L) × 4 cm (W) × 1 cm (H) → $4 \times 4 \times 1 = 16$

Total volume = 24 + 8 + 16 = 48 cm³

✔ Answer: 48 cm³

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5)

This is an L-shaped prism.

Break into two cuboids:

- Vertical part: 5 cm (L) × 2 cm (W) × 5 cm (H) → $5 \times 2 \times 5 = 50$
- Horizontal part: 7 cm (L) × 1 cm (W) × 3 cm (H) → $7 \times 1 \times 3 = 21$

Wait — but they overlap? Let's see.

The vertical part is 5 cm long, 2 cm wide, 5 cm high.

The horizontal part is attached at the base, extending 7 cm long, 1 cm wide, 3 cm high.

But where do they meet?

From diagram:
- The vertical part is 5 cm long, 2 cm wide, 5 cm high.
- The horizontal part is 7 cm long, 1 cm wide, 3 cm high.
- They share a 5 cm × 1 cm area.

But the horizontal part has only 1 cm width, while the vertical part has 2 cm width.

So likely:
- Vertical block: 5 cm (L) × 2 cm (W) × 5 cm (H) → $5 \times 2 \times 5 = 50$
- Horizontal block: 7 cm (L) × 1 cm (W) × 3 cm (H) → $7 \times 1 \times 3 = 21$

But do they overlap? Yes — the horizontal block starts at the end of the vertical block.

But the vertical block is 5 cm long, and the horizontal block is 7 cm long — but they connect at a common 5 cm segment?

Wait — the horizontal block is 7 cm long, but only 1 cm wide, and it's attached to the vertical block.

The vertical block is 5 cm long, 2 cm wide, 5 cm high.

The horizontal block is 7 cm long, 1 cm wide, 3 cm high — but it's only 3 cm high, so it doesn't reach the full height.

But the connection is at the base.

But the horizontal block has a length of 7 cm, and the vertical block has length of 5 cm.

But from the diagram, the horizontal block appears to extend from the vertical block.

Wait — the dashed line suggests the horizontal block goes under.

Actually, the horizontal block is attached to the base of the vertical block.

But the horizontal block is 3 cm high, and the vertical block is 5 cm high, so the horizontal block is shorter.

But the horizontal block is 7 cm long, and the vertical block is 5 cm long.

So the horizontal block extends 2 cm beyond the vertical block.

But they share a 5 cm × 1 cm × 3 cm region.

So total volume = vertical + horizontal = $5 \times 2 \times 5 = 50$, plus $7 \times 1 \times 3 = 21$, but subtract the overlapping part?

No — they don’t overlap in space. The horizontal block is only 1 cm wide, and the vertical block is 2 cm wide — so they are adjacent.

But the horizontal block is on the same base as the vertical block, but only 1 cm wide.

So:
- Vertical block: 5 cm (L) × 2 cm (W) × 5 cm (H) → $5 \times 2 \times 5 = 50$
- Horizontal block: 7 cm (L) × 1 cm (W) × 3 cm (H) → $7 \times 1 \times 3 = 21$

But do they share a region? Yes — the horizontal block shares a 5 cm × 1 cm × 3 cm region with the base of the vertical block? But the vertical block is 5 cm high, so the horizontal block is below it.

Wait — no — the horizontal block is attached to the side of the vertical block?

Wait — the diagram shows:
- Vertical block: 5 cm long, 2 cm wide, 5 cm high
- Horizontal block: 7 cm long, 1 cm wide, 3 cm high
- Connected at the base — the horizontal block extends from the bottom of the vertical block.

But the horizontal block is only 3 cm high, so it doesn’t go up to the top.

And the vertical block is 5 cm high.

But the overlap in base: the horizontal block is 1 cm wide, and the vertical block is 2 cm wide — so they are adjacent.

So no overlapping volume.

So total volume = 50 + 21 = 71 cm³

But wait — is the horizontal block entirely separate? Or does it extend under the vertical block?

From the dashed line, it seems the horizontal block is attached to the base of the vertical block, but extends out.

But since the vertical block is 2 cm wide and the horizontal block is 1 cm wide, they are side-by-side.

So total volume = 50 + 21 = 71 cm³

✔ Answer: 71 cm³

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6)

This is a large cuboid with a hole in it.

We can compute:
- Volume of outer cuboid
- Minus volume of inner hole

Outer cuboid:
- Length: 8 cm
- Width: 6 cm
- Height: 4 cm
→ Volume = $8 \times 6 \times 4 = 192$ cm³

Inner hole:
- From diagram: a rectangular prism removed from the center.
- Dimensions: 4 cm (length) × 2 cm (width) × 4 cm (height)? Wait — the hole is shown as 4 cm × 2 cm, and depth is not given.

Wait — the hole is drawn with:
- 4 cm (length)
- 2 cm (width)
- And depth — but the hole goes through the entire depth? The outer box is 6 cm wide, and the hole is 2 cm wide.

But the depth of the hole — is it the full 6 cm?

Wait — the hole is shown as a rectangle inside, with 4 cm and 2 cm — but we need to know if it's a cavity going through.

But the hole is not a full-through hole — it's a rectangular cavity.

From the diagram:
- The hole has:
- Length: 4 cm
- Width: 2 cm
- Depth: ? — but the depth is the same as the box depth, which is 6 cm?

Wait — the box is 6 cm high, 8 cm long, 4 cm deep.

Wait — labels:
- Top: 8 cm (length)
- Side: 6 cm (height)
- Depth: 4 cm (from side view)

So the box is:
- L = 8 cm
- H = 6 cm
- D = 4 cm

So volume = $8 \times 6 \times 4 = 192$ cm³

Now the hole: it's a rectangular prism inside, with:
- Length: 4 cm
- Width: 2 cm
- Depth: ? — but the hole is shown as going from front to back? Or just in the middle?

From the diagram, the hole is in the center, and the depth is the same as the box depth? But the box depth is 4 cm.

Wait — the hole is drawn with:
- 4 cm (length)
- 2 cm (width)
- And the depth is 4 cm? Because it's shown as a rectangle going through.

But the box is 4 cm deep, so the hole goes through the full depth.

So the hole is:
- 4 cm (L) × 2 cm (W) × 4 cm (D) → $4 \times 2 \times 4 = 32$ cm³

Wait — but the hole is not a full cylinder; it's a rectangular cavity.

But is the depth 4 cm? Yes — the box is 4 cm deep, so the cavity is 4 cm deep.

But wait — the height of the hole? The hole is shown as 4 cm in height? But the box is 6 cm high.

Wait — the hole is shown with:
- 4 cm (length)
- 2 cm (width)
- And it's inside — but how high?

From the diagram, the hole is not full height — it's only 4 cm high? But the box is 6 cm high.

Wait — the hole is shown as a rectangle with 4 cm and 2 cm — but we need to know its height.

But the diagram shows:
- The hole has a vertical side of 4 cm — so height = 4 cm?
- Width = 2 cm
- Depth = 4 cm

So volume of hole = $4 \times 2 \times 4 = 32$ cm³

But the box is 6 cm high, so the hole is only 4 cm high — so it's not full height.

So total volume = outer – hole = $192 - 32 = 160$ cm³

Wait — but is the hole really 4 cm high? Yes — the diagram shows a 4 cm vertical line.

So hole is 4 cm (L) × 2 cm (W) × 4 cm (H) → $4 \times 2 \times 4 = 32$

Box: 8×6×4 = 192

So volume = 192 - 32 = 160 cm³

✔ Answer: 160 cm³

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✔ Final Answers:

1) 24 cm³
2) 48 cm³
3) 66 cm³
4) 48 cm³
5) 71 cm³
6) 160 cm³

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