Find the total volume of composite rectangular prisms in this math worksheet.
A worksheet titled "Volume of Composite Rectangular Prisms" with four diagrams (a, b, c, d) showing composite figures made of rectangular prisms, each with labeled dimensions and a space to calculate the total volume.
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Step-by-step solution for: Volume of Composite Rectangular Prism Worksheets (answers ...
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Show Answer Key & Explanations
Step-by-step solution for: Volume of Composite Rectangular Prism Worksheets (answers ...
To solve the problem of finding the total volume of the composite rectangular prisms, we need to break each figure into individual rectangular prisms, calculate the volume of each prism, and then sum the volumes. Let's go through each part step by step.
---
The figure consists of two rectangular prisms stacked on top of each other.
1. Top Prism:
- Dimensions: \( 14 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 14 \times 3 \times 5 = 210 \, \text{cm}^3
\]
2. Bottom Prism:
- Dimensions: \( 14 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 14 \times 3 \times 5 = 210 \, \text{cm}^3
\]
3. Total Volume:
\[
V_{\text{total}} = V_{\text{top}} + V_{\text{bottom}} = 210 + 210 = 420 \, \text{cm}^3
\]
Answer for (a):
\[
\boxed{420}
\]
---
The figure consists of three rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 15 \, \text{in} \times 4 \, \text{in} \times 6 \, \text{in} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 15 \times 4 \times 6 = 360 \, \text{in}^3
\]
2. Middle Prism:
- Dimensions: \( 7 \, \text{in} \times 4 \, \text{in} \times 3 \, \text{in} \)
- Volume:
\[
V_{\text{middle}} = \text{length} \times \text{width} \times \text{height} = 7 \times 4 \times 3 = 84 \, \text{in}^3
\]
3. Top Prism:
- Dimensions: \( 7 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 7 \times 3 \times 3 = 63 \, \text{in}^3
\]
4. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{middle}} + V_{\text{top}} = 360 + 84 + 63 = 507 \, \text{in}^3
\]
Answer for (b):
\[
\boxed{507}
\]
---
The figure consists of two rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 10 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 2 = 60 \, \text{cm}^3
\]
2. Top Prism:
- Dimensions: \( 6 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 6 \times 3 \times 4 = 72 \, \text{cm}^3
\]
3. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{top}} = 60 + 72 = 132 \, \text{cm}^3
\]
Answer for (c):
\[
\boxed{132}
\]
---
The figure consists of three rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 10 \, \text{m} \times 8 \, \text{m} \times 12 \, \text{m} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 10 \times 8 \times 12 = 960 \, \text{m}^3
\]
2. Middle Prism:
- Dimensions: \( 8 \, \text{m} \times 1 \, \text{m} \times 6 \, \text{m} \)
- Volume:
\[
V_{\text{middle}} = \text{length} \times \text{width} \times \text{height} = 8 \times 1 \times 6 = 48 \, \text{m}^3
\]
3. Top Prism:
- Dimensions: \( 8 \, \text{m} \times 1 \, \text{m} \times 6 \, \text{m} \) (same as the middle prism)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 8 \times 1 \times 6 = 48 \, \text{m}^3
\]
4. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{middle}} + V_{\text{top}} = 960 + 48 + 48 = 1056 \, \text{m}^3
\]
Answer for (d):
\[
\boxed{1056}
\]
---
\[
\boxed{420, 507, 132, 1056}
\]
---
Part (a)
The figure consists of two rectangular prisms stacked on top of each other.
1. Top Prism:
- Dimensions: \( 14 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 14 \times 3 \times 5 = 210 \, \text{cm}^3
\]
2. Bottom Prism:
- Dimensions: \( 14 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 14 \times 3 \times 5 = 210 \, \text{cm}^3
\]
3. Total Volume:
\[
V_{\text{total}} = V_{\text{top}} + V_{\text{bottom}} = 210 + 210 = 420 \, \text{cm}^3
\]
Answer for (a):
\[
\boxed{420}
\]
---
Part (b)
The figure consists of three rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 15 \, \text{in} \times 4 \, \text{in} \times 6 \, \text{in} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 15 \times 4 \times 6 = 360 \, \text{in}^3
\]
2. Middle Prism:
- Dimensions: \( 7 \, \text{in} \times 4 \, \text{in} \times 3 \, \text{in} \)
- Volume:
\[
V_{\text{middle}} = \text{length} \times \text{width} \times \text{height} = 7 \times 4 \times 3 = 84 \, \text{in}^3
\]
3. Top Prism:
- Dimensions: \( 7 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 7 \times 3 \times 3 = 63 \, \text{in}^3
\]
4. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{middle}} + V_{\text{top}} = 360 + 84 + 63 = 507 \, \text{in}^3
\]
Answer for (b):
\[
\boxed{507}
\]
---
Part (c)
The figure consists of two rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 10 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 2 = 60 \, \text{cm}^3
\]
2. Top Prism:
- Dimensions: \( 6 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} \)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 6 \times 3 \times 4 = 72 \, \text{cm}^3
\]
3. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{top}} = 60 + 72 = 132 \, \text{cm}^3
\]
Answer for (c):
\[
\boxed{132}
\]
---
Part (d)
The figure consists of three rectangular prisms.
1. Bottom Prism:
- Dimensions: \( 10 \, \text{m} \times 8 \, \text{m} \times 12 \, \text{m} \)
- Volume:
\[
V_{\text{bottom}} = \text{length} \times \text{width} \times \text{height} = 10 \times 8 \times 12 = 960 \, \text{m}^3
\]
2. Middle Prism:
- Dimensions: \( 8 \, \text{m} \times 1 \, \text{m} \times 6 \, \text{m} \)
- Volume:
\[
V_{\text{middle}} = \text{length} \times \text{width} \times \text{height} = 8 \times 1 \times 6 = 48 \, \text{m}^3
\]
3. Top Prism:
- Dimensions: \( 8 \, \text{m} \times 1 \, \text{m} \times 6 \, \text{m} \) (same as the middle prism)
- Volume:
\[
V_{\text{top}} = \text{length} \times \text{width} \times \text{height} = 8 \times 1 \times 6 = 48 \, \text{m}^3
\]
4. Total Volume:
\[
V_{\text{total}} = V_{\text{bottom}} + V_{\text{middle}} + V_{\text{top}} = 960 + 48 + 48 = 1056 \, \text{m}^3
\]
Answer for (d):
\[
\boxed{1056}
\]
---
Final Answers
\[
\boxed{420, 507, 132, 1056}
\]
Parent Tip: Review the logic above to help your child master the concept of finding volume of irregular shapes worksheet.
