Volume of Composite Figures Additive Volume - Worksheets - Free Printable

You’ve uploaded a worksheet titled “Volume of Composite Figures”, which asks you to find the volume of 3D shapes made by combining two or more rectangular prisms.

I’ll solve each problem shown in the images and explain step-by-step.

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## 🔹 Problem 1: “Volume of Composite Figures” – Figure a

This is an L-shaped prism. We can split it into two rectangular prisms.

Step 1: Split the shape

We can divide it into:
- Part 1 (Top left block): Dimensions = 6 m (length) × 4 m (width) × 5 m (height)
- Part 2 (Bottom right block): Dimensions = 9 m (length) × 5 m (width) × 3 m (height)

> Note: The total length is 9 m, so the bottom part’s length is 9 m. The top part’s width is 4 m, and the vertical drop is 5 m — so the bottom part’s height is 3 m.

Step 2: Calculate Volume of Each Part

Volume of Part 1:
> 6 m × 4 m × 5 m = 120 m³

Volume of Part 2:
> 9 m × 5 m × 3 m = 135 m³

Step 3: Add Volumes Together

Total Volume = 120 + 135 = 255 m³

✔ Answer for a: 255 m³

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## 🔹 Problem 2: “Volume of Composite Figures” – Figure b

This is a rectangular prism with a smaller rectangular prism cut out from the corner.

Step 1: Find Volume of the Whole Prism (without cutout)

Dimensions: 10 cm × 7 cm × 5 cm
Volume = 10 × 7 × 5 = 350 cm³

Step 2: Find Volume of the Cutout Piece

The cutout has dimensions: 6 cm × 4 cm × 2 cm
Volume = 6 × 4 × 2 = 48 cm³

Step 3: Subtract Cutout Volume from Whole

Total Volume = 350 - 48 = 302 cm³

✔ Answer for b: 302 cm³

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## 🔹 Problem 3: “Volume of the Building”

This building is made of two rectangular prisms joined together:

- Left tower: 4 m (width) × 6 m (depth) × 8 m (height)
- Right wing: 8 m (width) × 6 m (depth) × 4 m (height)

> Note: The diagram shows the building has two parts — one taller (left) and one shorter (right). The depth (front-to-back) is 6 m for both.

Step 1: Volume of Left Tower

4 m × 6 m × 8 m = 192 m³

Step 2: Volume of Right Wing

8 m × 6 m × 4 m = 192 m³

Step 3: Total Volume

192 + 192 = 384 m³

✔ Answer for Building: 384 m³

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## 🔹 Problem 4: “Volume of Composite Figures” – Figure a (with fill-in blanks)

This is another composite figure — looks like a large base with a smaller block on top.

Given dimensions:

- Base: 9 m × 9 m × 6 m
- Top block: 10 m × 6 m × 3 m

Wait — let’s check alignment.

Actually, looking at the diagram:

- The bottom part is 9 m (length) × 9 m (width) × 6 m (height)
- The top part is placed on top, but only covers part of the base. Its dimensions are 10 m (length) × 6 m (width) × 3 m (height)

But wait — 10 m length? The base is only 9 m long. This suggests the top part overhangs slightly, which is unusual. Let’s re-express based on standard interpretation.

Alternatively, perhaps the top part is 6 m (width) × 3 m (height), and its length is 10 m — but that doesn’t align with the 9 m base.

Let me reinterpret using the labels:

From the diagram:

- The base is 9 m × 9 m × 6 m → volume = 9×9×6 = 486 m³
- The top part is 10 m × 6 m × 3 m → volume = 10×6×3 = 180 m³

But if they’re stacked, we must ensure no overlap. Since the top part is wider (10m vs 9m), it likely extends beyond the base — which is acceptable in math problems.

So total volume = 486 + 180 = 666 m³

However, let’s look at the worksheet’s fill-in blanks:

> Volume of part 1: ___ × ___ × ___ = ___ m³
> Volume of part 2: ___ × ___ × ___ = ___ m³
> Volume of shape: ___ + ___ = ___ m³

It’s expecting you to split the shape into two parts.

Looking again — perhaps the shape is meant to be divided as:

- Part 1 (bottom): 9 m × 9 m × 6 m → 486 m³
- Part 2 (top): 10 m × 6 m × 3 m → 180 m³

Even though there’s an overhang, we still add them.

✔ So fill in:

Volume of part 1:
9 × 9 × 6 = 486 m³

Volume of part 2:
10 × 6 × 3 = 180 m³

Volume of shape:
486 + 180 = 666 m³

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| a (L-shape) | 255 m³ |
| b (cutout) | 302 cm³ |
| Building | 384 m³ |
| Composite with blanks | 666 m³ |

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## 💡 Key Concept Reminder:

To find the volume of a composite figure made of rectangular prisms:
- Break it into separate rectangular prisms.
- Calculate the volume of each using V = l × w × h.
- Add volumes if parts are joined together.
- Subtract if one part is removed (like a cutout).

Let me know if you’d like diagrams or visual breakdowns too!