Let's solve each composite rectangular prism problem step by step. We'll break each figure into simpler rectangular prisms, calculate the volume of each part, and then add them together.
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Formula for Volume of a Rectangular Prism:
$$
V = \text{length} \times \text{width} \times \text{height}
$$
---
a.
This figure consists of two rectangular prisms stacked vertically.
-
Bottom prism:
- Length = 14 cm
- Width = 3 cm
- Height = 5 cm
$$
V_1 = 14 \times 3 \times 5 = 210\ \text{cm}^3
$$
-
Top prism:
- Length = 14 cm
- Width = 3 cm
- Height = 5 cm
$$
V_2 = 14 \times 3 \times 5 = 210\ \text{cm}^3
$$
Total Volume:
$$
V = 210 + 210 = \boxed{420\ \text{cm}^3}
$$
---
b.
This figure has two prisms side by side.
-
Left prism (larger base):
- Length = 15 in
- Width = 4 in
- Height = 6 in
$$
V_1 = 15 \times 4 \times 6 = 360\ \text{in}^3
$$
-
Right prism (smaller top):
- Length = 7 in
- Width = 3 in
- Height = 3 in
$$
V_2 = 7 \times 3 \times 3 = 63\ \text{in}^3
$$
Total Volume:
$$
V = 360 + 63 = \boxed{423\ \text{in}^3}
$$
---
c.
This figure has two prisms: a long horizontal one and a smaller vertical one on top.
-
Bottom prism (long base):
- Length = 10 cm
- Width = 3 cm
- Height = 2 cm
$$
V_1 = 10 \times 3 \times 2 = 60\ \text{cm}^3
$$
-
Top prism (smaller box):
- Length = 6 cm
- Width = 3 cm
- Height = 4 cm
$$
V_2 = 6 \times 3 \times 4 = 72\ \text{cm}^3
$$
Total Volume:
$$
V = 60 + 72 = \boxed{132\ \text{cm}^3}
$$
---
d.
This figure has two prisms: a large one at the bottom and a smaller one on top to the left.
-
Bottom prism:
- Length = 10 m
- Width = 3 m
- Height = 6 m
$$
V_1 = 10 \times 3 \times 6 = 180\ \text{m}^3
$$
-
Top prism:
- Length = 8 m
- Width = 3 m
- Height = 12 m – 6 m = 6 m (since total height is 12 m, and bottom is 6 m)
$$
V_2 = 8 \times 3 \times 6 = 144\ \text{m}^3
$$
Total Volume:
$$
V = 180 + 144 = \boxed{324\ \text{m}^3}
$$
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✔ Final Answers:
a. $ \boxed{420\ \text{cm}^3} $
b. $ \boxed{423\ \text{in}^3} $
c. $ \boxed{132\ \text{cm}^3} $
d. $ \boxed{324\ \text{m}^3} $
Let me know if you'd like a visual breakdown or explanation of how to identify the parts!
Parent Tip: Review the logic above to help your child master the concept of additive volume 5th grade worksheet.
