Volume of Composite Figures Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific composite shapes in your uploaded image. However, I can guide you through solving volume of composite shapes problems step by step and help you apply the method to your task.

---

🔷 What is a Composite Shape?

A composite shape is made up of two or more basic 3D geometric shapes (like cylinders, cones, prisms, pyramids, spheres, etc.). To find its total volume, you:

1. Break it down into simpler shapes.
2. Find the volume of each individual shape.
3. Add or subtract volumes as needed (e.g., if one shape is hollowed out).
4. Round to the nearest tenth (as requested).

---

🔷 Common Volume Formulas

| Shape | Volume Formula |
|-------------|----------------|
| Rectangular Prism | $ V = l \times w \times h $ |
| Cylinder | $ V = \pi r^2 h $ |
| Cone | $ V = \frac{1}{3} \pi r^2 h $ |
| Sphere | $ V = \frac{4}{3} \pi r^3 $ |
| Pyramid | $ V = \frac{1}{3} \times \text{Base Area} \times h $ |
| Triangular Prism | $ V = \frac{1}{2} \times b \times h_{\text{triangle}} \times l $ |

> Use $ \pi \approx 3.14 $ unless otherwise specified.

---

🔷 Example Problem (Illustrative)

Let’s assume one of the shapes in your image is a cylinder with a cone on top, like a silo.

- Cylinder: radius = 3 cm, height = 8 cm
- Cone: same radius = 3 cm, height = 5 cm

#### Step 1: Volume of Cylinder
$$
V_{\text{cyl}} = \pi r^2 h = 3.14 \times 3^2 \times 8 = 3.14 \times 9 \times 8 = 226.08 \text{ cm}^3
$$

#### Step 2: Volume of Cone
$$
V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times 9 \times 5 = 47.1 \text{ cm}^3
$$

#### Step 3: Total Volume
$$
V_{\text{total}} = 226.08 + 47.1 = 273.18 \approx \boxed{273.2} \text{ cm}^3
$$

---

✔ How to Solve Your Image Task:

For each shape in your image:

1. Identify the individual components (e.g., prism + pyramid).
2. Measure dimensions (radius, height, length, width, etc.) from the diagram.
3. Apply formulas for each part.
4. Add/subtract appropriately.
5. Round to one decimal place.

---

📌 Tips:

- If a shape has a hole, subtract the inner volume.
- Check units — ensure all measurements are in the same unit.
- Double-check which parts are attached vs. removed.

---

👉 Please describe the shapes in your image (e.g., "a rectangular prism with a pyramid on top", or "a cylinder with a hemisphere on top"), and I’ll walk you through the exact solution!