Volume Of Composite Figures | 52 plays | Quizizz - Free Printable

You’ve uploaded an image with four 3D composite shapes (labeled 5, 6, 7, and 8), each with dimensions given. The implied task — based on common math problems involving such diagrams — is to find the volume of each shape.

Since these are composite solids, we’ll break each into simpler rectangular prisms (or cuboids), calculate their individual volumes, and then add or subtract as needed.

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## 🔢 GENERAL FORMULA:
> Volume of a rectangular prism = length × width × height

We’ll apply this to each part.

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# ✔ SHAPE 5

*Dimensions: overall 7 in long, 5 in wide, 6 in tall. The top left portion is 4 in high, and the bottom right is 3 in high.*

Strategy:

This is an L-shape. We can split it into two rectangular prisms:

#### Option A: Split vertically
- Left vertical block: 2 in (width) × 5 in (depth) × 6 in (height)
- Bottom horizontal block: 5 in (length) × 5 in (depth) × 3 in (height)

Wait — let’s check dimensions again:

Actually, total length = 7 in. The top part is 4 in high, and the bottom part is 3 in high. The step happens at 2 in from the left? Let's look:

From the diagram:
- Total height = 6 in
- Lower part height = 3 in
- Upper part height = 4 in → so the “step” is 1 in high? That doesn’t make sense.

Wait — better interpretation:

It’s a stepped block. Think of it as:

- Base block: 7 in (L) × 5 in (W) × 3 in (H)
- Top-left block: 2 in (L) × 5 in (W) × 3 in (H) — because 6 - 3 = 3 in added height on the left?

Wait — no. Let me re-read:

The top section is labeled “4 in” — that’s likely the height of the top portion. But total height is 6 in. So the lower portion is 3 in high, and the upper portion is 4 in high? That would mean overlapping.

Actually, standard way: This is a right L-shape. The full depth is 5 in.

Let’s split into two parts:

#### Part 1: Bottom full rectangle
- Length = 7 in, Width = 5 in, Height = 3 in
→ Volume = 7 × 5 × 3 = 105 in³

#### Part 2: Top left rectangle (on top of the left 2 in of the base)
- Length = 2 in, Width = 5 in, Height = 3 in (because 6 - 3 = 3 in added on top)
→ Volume = 2 × 5 × 3 = 30 in³

✔ Total Volume = 105 + 30 = 135 in³

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# ✔ SHAPE 6

*Dimensions: Base is 14 cm long, 7 cm wide, 2 cm high. Top center block is 8 cm high, 4 cm wide, and 7 cm deep?*

Actually, looking at labels:

- Base: 14 cm (length), 7 cm (width), 2 cm (height)
- Top part: 8 cm (height), 4 cm (width), and depth is same as base? Probably 7 cm.

But the top sits centered? The base is 14 cm long, top is 4 cm wide — so it must be centered.

So:

#### Part 1: Base
- 14 × 7 × 2 = 196 cm³

#### Part 2: Top block
- 4 × 7 × 8 = 224 cm³

✔ Total Volume = 196 + 224 = 420 cm³

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# ✔ SHAPE 7

*Overall: 9 ft long, 6 ft high, 3 ft deep. Cutout: 5 ft long, 2 ft high, 3 ft deep.*

This is a rectangular block with a rectangular hole cut out.

#### Full outer block:
- 9 ft × 6 ft × 3 ft = 162 ft³

#### Cutout (missing part):
- 5 ft × 2 ft × 3 ft = 30 ft³

✔ Volume = 162 - 30 = 132 ft³

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# ✔ SHAPE 8

*Overall: 10 in long, 11 in high, 5 in deep. Cutout: 3 in wide, 7 in high, 5 in deep.*

Again, a solid with a rectangular cutout.

#### Full outer block (if solid):
- 10 in × 11 in × 5 in = 550 in³

#### Cutout (removed part):
- 3 in × 7 in × 5 in = 105 in³

✔ Volume = 550 - 105 = 445 in³

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## 📦 FINAL ANSWERS:

| Shape | Volume |
|-------|-----------------|
| 5 | 135 in³ |
| 6 | 420 cm³ |
| 7 | 132 ft³ |
| 8 | 445 in³ |

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## 🧠 EXPLANATION SUMMARY:

- For composite shapes, break them into simple rectangular prisms.
- For shapes with holes/cutouts, compute the volume of the full block minus the volume of the removed part.
- Always ensure units match and multiply length × width × height for each part.

Let me know if you want surface area too, or if you meant a different task!