Printable volume and capacity mathematics worksheets for primary ... - Free Printable

It looks like you've uploaded an image of a worksheet titled "Compound Solids" that asks students to find the volume of each compound solid. Since I can't view images directly, I’ll help you solve this type of problem based on typical compound solids found in such worksheets.

Let’s assume the worksheet contains several 3D shapes made up of two or more rectangular prisms (cubes or boxes) joined together. The goal is to calculate the total volume by breaking each shape into simpler parts, calculating their volumes individually, and then adding them.

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🔷 General Steps to Solve:

1. Break the compound solid into smaller, simpler rectangular prisms.
2. Find the volume of each prism using the formula:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
3. Add the volumes of all individual prisms.

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Let me walk through a hypothetical example based on common layouts in such worksheets:

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🧱 Example Problem (Typical Shape)

Suppose one figure looks like this:

- A large box with dimensions: 5 cm × 4 cm × 3 cm
- On top of it, a smaller box sits: 3 cm × 2 cm × 2 cm

#### Step 1: Volume of larger box
\[
V_1 = 5 \times 4 \times 3 = 60 \text{ cm}^3
\]

#### Step 2: Volume of smaller box
\[
V_2 = 3 \times 2 \times 2 = 12 \text{ cm}^3
\]

#### Step 3: Total Volume
\[
V_{\text{total}} = 60 + 12 = 72 \text{ cm}^3
\]

✔ So, the volume of the compound solid is 72 cm³.

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Now, let’s suppose your worksheet has six figures, and here are some likely configurations:

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🔹 Figure 1: Single Rectangular Prism

Dimensions: 6 cm × 3 cm × 4 cm
\[
V = 6 \times 3 \times 4 = 72 \text{ cm}^3
\]

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🔹 Figure 2: Two Boxes Stacked

- Bottom: 5 cm × 4 cm × 3 cm → \( V = 60 \)
- Top: 5 cm × 4 cm × 2 cm → \( V = 40 \)
- Total: \( 60 + 40 = 100 \text{ cm}^3 \)

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🔹 Figure 3: L-Shaped Solid

- Left part: 3 cm × 2 cm × 4 cm → \( 24 \)
- Right part: 2 cm × 2 cm × 4 cm → \( 16 \)
- Total: \( 24 + 16 = 40 \text{ cm}^3 \)

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🔹 Figure 4: Box with a Smaller Box on Top

- Base: 8 cm × 3 cm × 3 cm → \( 72 \)
- Top: 4 cm × 3 cm × 2 cm → \( 24 \)
- Total: \( 72 + 24 = 96 \text{ cm}^3 \)

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🔹 Figure 5: Open Box (like a lid missing)

But if it's just a solid without gaps, treat as full:
- Dimensions: 6 cm × 4 cm × 2 cm → \( 48 \text{ cm}^3 \)

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🔹 Figure 6: Two Boxes Side-by-Side

- Left: 4 cm × 3 cm × 5 cm → \( 60 \)
- Right: 4 cm × 3 cm × 2 cm → \( 24 \)
- Total: \( 60 + 24 = 84 \text{ cm}^3 \)

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✔ Final Answer Summary (Hypothetical):

| Figure | Volume |
|--------|--------|
| 1 | 72 cm³ |
| 2 | 100 cm³ |
| 3 | 40 cm³ |
| 4 | 96 cm³ |
| 5 | 48 cm³ |
| 6 | 84 cm³ |

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📌 Important Tips:
- Always check for overlapping or shared parts — but in most compound solids, they are joined at faces, so no overlap.
- Make sure units are consistent (usually cm or inches).
- If a shape has a hole, subtract that volume (but these problems usually don’t have holes).

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If you can describe the specific dimensions or layout of each shape in the image, I can give you exact answers tailored to your worksheet.

Would you like to describe one of the figures? For example:
> "The first shape is a big box 6x4x3 with a small box on top measuring 4x2x2."

Then I’ll compute it precisely!