Volume of Composite Rectangular Prism Worksheets (answers ... - Free Printable

Let's solve each composite rectangular prism problem step by step. The volume of a rectangular prism is calculated using the formula:

$$
V = \text{length} \times \text{width} \times \text{height}
$$

For composite figures, we break them into simpler rectangular prisms, calculate the volume of each, and then add them together.

---

a.

This figure consists of two stacked rectangles:
- Bottom part: 14 cm (length), 3 cm (width), 5 cm (height)
- Top part: 14 cm (length), 3 cm (width), 5 cm (height)

Wait — both parts are identical?

Actually, looking closely:
- The total height is 5 + 5 = 10 cm, but the bottom block has a height of 5 cm and the top one also 5 cm.
- Both have the same base: 14 cm × 3 cm

So:
- Volume of bottom = $14 \times 3 \times 5 = 210\ \text{cm}^3$
- Volume of top = $14 \times 3 \times 5 = 210\ \text{cm}^3$

Total volume:
$$
V = 210 + 210 = \boxed{420\ \text{cm}^3}
$$

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b.

This shape has two parts:
- A larger base prism: length = 15 in, width = 4 in, height = 6 in
- A smaller prism on top: length = 7 in, width = 4 in, height = 3 in

Note: The smaller prism sits on top of the larger one, so it’s not overlapping in volume.

Volume of base:
$$
V_1 = 15 \times 4 \times 6 = 360\ \text{in}^3
$$

Volume of top:
$$
V_2 = 7 \times 4 \times 3 = 84\ \text{in}^3
$$

Total volume:
$$
V = 360 + 84 = \boxed{444\ \text{in}^3}
$$

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c.

This shape has two parts:
- Left part: length = 10 cm, width = 3 cm, height = 2 cm
- Right part: length = 6 cm, width = 3 cm, height = 4 cm

But wait — the left part is only 2 cm high, and the right part is 4 cm high. But the base width is 3 cm for both.

Let’s check dimensions carefully:
- The bottom layer is 10 cm long, 3 cm wide, and 2 cm high → that’s the base
- On top of the right side, there’s an extension that adds another 2 cm height (from 2 to 4 cm), but only over 6 cm length.

So:
- Base (bottom): $10 \times 3 \times 2 = 60\ \text{cm}^3$
- Top part (on right): $6 \times 3 \times 2 = 36\ \text{cm}^3$ ← because only the extra 2 cm height is added

Wait — actually, the total height of the right side is 4 cm, and the bottom is 2 cm, so the top piece is 2 cm tall, 6 cm long, and 3 cm wide.

Yes.

So:
- Volume of lower part: $10 \times 3 \times 2 = 60\ \text{cm}^3$
- Volume of upper part: $6 \times 3 \times 2 = 36\ \text{cm}^3$

Total:
$$
V = 60 + 36 = \boxed{96\ \text{cm}^3}
$$

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d.

This shape has two parts:
- Bottom part: 10 m (length), 3 m (width), 6 m (height)
- Top part: 8 m (length), 3 m (width), 6 m (height) ← since total height is 12 m, and bottom is 6 m, top is 6 m high

Wait — but the top part is placed on the left side, and its length is 8 m, while the base is 10 m long.

Let’s analyze:
- Bottom: full length 10 m, width 3 m, height 6 m
- Top: placed on top of the left side, length 8 m, width 3 m, height 6 m

So:
- Volume of bottom: $10 \times 3 \times 6 = 180\ \text{m}^3$
- Volume of top: $8 \times 3 \times 6 = 144\ \text{m}^3$

Total:
$$
V = 180 + 144 = \boxed{324\ \text{m}^3}
$$

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✔ Final Answers:

a. $ V = \boxed{420}\ \text{cm}^3 $
b. $ V = \boxed{444}\ \text{in}^3 $
c. $ V = \boxed{96}\ \text{cm}^3 $
d. $ V = \boxed{324}\ \text{m}^3 $

Let me know if you'd like diagrams or explanations for any part!