This worksheet provides practice problems for calculating the volume of composite rectangular prisms by breaking them down into simpler shapes.

To find the total volume of composite rectangular prisms, we break each figure into separate rectangular prisms (boxes), calculate the volume of each using the formula:

> Volume = Length × Width × Height

Then, we add the volumes together.

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a.

This figure is made of two identical rectangular prisms stacked vertically.

Each prism has:
- Length = 14 cm
- Width = 3 cm
- Height = 5 cm

Volume of one prism = 14 × 3 × 5 = 210 cm³

Since there are two, total volume = 210 × 2 = 420 cm³

✔ Answer: V = 420 cm³

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b.

This is a step-like figure. We can split it into two rectangular prisms:

#### Bottom prism:
- Length = 15 in
- Width = 4 in
- Height = 6 in
→ Volume = 15 × 4 × 6 = 360 in³

#### Top prism (on the right):
- Length = 7 in
- Width = 4 in (same as bottom)
- Height = 3 in
→ Volume = 7 × 4 × 3 = 84 in³

Total volume = 360 + 84 = 444 in³

✔ Answer: V = 444 in³

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c.

This is an L-shaped figure. Split into two prisms:

#### Bottom prism (longer part):
- Length = 10 cm
- Width = 3 cm
- Height = 2 cm
→ Volume = 10 × 3 × 2 = 60 cm³

#### Top prism (on the left):
- Length = 6 cm (only the left part sticks up)
- Width = 3 cm
- Height = 4 cm
→ Volume = 6 × 3 × 4 = 72 cm³

Total volume = 60 + 72 = 132 cm³

✔ Answer: V = 132 cm³

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d.

This is another step-like figure. Split into two prisms:

#### Bottom prism:
- Length = 10 m
- Width = 3 m
- Height = 6 m
→ Volume = 10 × 3 × 6 = 180 m³

#### Top prism (on the left):
- Length = 8 m
- Width = 3 m
- Height = 12 – 6 = 6 m (since total height is 12m, and bottom is 6m)
→ Volume = 8 × 3 × 6 = 144 m³

Total volume = 180 + 144 = 324 m³

✔ Answer: V = 324 m³

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## ✔ Final Answers:

a. V = 420 cm³
b. V = 444 in³
c. V = 132 cm³
d. V = 324 m³

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Let me know if you’d like a diagram or visual breakdown for any of these!