Since I can't view or access uploaded images directly, I can't see the specific composite shapes in your image. However, I can guide you through solving
volume problems involving composite 3D shapes and help you apply the method to your task.
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🔷 What is a Composite Shape?
A
composite shape is made up of two or more basic 3D geometric solids (like prisms, pyramids, cylinders, cones, etc.). To find its total volume, you calculate the volume of each individual part and then add them together.
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✔ Step-by-Step Strategy:
1.
Identify the individual shapes that make up the composite figure.
- Common ones: rectangular prism, triangular prism, cylinder, pyramid, cone, etc.
2.
Find the volume of each shape using the appropriate formula:
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Rectangular Prism:
$ V = \text{length} \times \text{width} \times \text{height} $
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Triangular Prism:
$ V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{length} $
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Cylinder:
$ V = \pi r^2 h $
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Pyramid:
$ V = \frac{1}{3} \times \text{Base Area} \times \text{height} $
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Cone:
$ V = \frac{1}{3} \pi r^2 h $
3.
Add the volumes of all parts together.
4.
Round your answer to the nearest tenth as requested.
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🧩 Example Problem (Hypothetical):
Suppose one of the figures is a
rectangular prism with a pyramid on top:
- Prism: length = 6 cm, width = 4 cm, height = 5 cm
→ Volume = $ 6 \times 4 \times 5 = 120 \, \text{cm}^3 $
- Pyramid: base same as prism (6×4), height = 3 cm
→ Volume = $ \frac{1}{3} \times (6 \times 4) \times 3 = 24 \, \text{cm}^3 $
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Total Volume = $ 120 + 24 = 144 \, \text{cm}^3 $
Answer:
144.0 cm³
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📌 Tips:
- Make sure all units are consistent (e.g., all in cm).
- Look for hidden dimensions — sometimes the height of a pyramid or cone isn’t labeled directly.
- If a shape is cut out (like a hole), subtract its volume instead.
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👉 Please describe the shapes in your image (e.g., “a rectangular prism with a triangular prism on top”) or list the dimensions if visible, and I’ll walk you through solving it step by step!
Parent Tip: Review the logic above to help your child master the concept of composite figure volume worksheet.
