Worksheets for calculating the volume of compound shapes with labeled dimensions.
Two worksheets titled "Calculating the Volume of Compound Shapes" showing four different 3D compound shapes with dimensions, each requiring volume calculation.
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Step-by-step solution for: Fifth Grade Volume Is Additive: Calculating the Volume of Compound ...
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Show Answer Key & Explanations
Step-by-step solution for: Fifth Grade Volume Is Additive: Calculating the Volume of Compound ...
To solve the problem of calculating the volume of compound shapes, we need to break each shape into simpler geometric shapes (like cubes and rectangular prisms), calculate the volume of each individual shape, and then sum the volumes. Let's go through each problem step by step.
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The compound shape consists of two rectangular prisms stacked on top of each other.
- Top Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 3 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 3 = 24 \, \text{in}^3 \).
- Bottom Prism: Dimensions are \(8 \, \text{in} \times 5 \, \text{in} \times 6 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 5 \times 6 = 240 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 24 + 240 = 264 \, \text{in}^3
\]
Answer for Problem 1: \(\boxed{264 \, \text{in}^3}\)
---
The compound shape consists of a rectangular prism with a smaller cube cut out from one corner.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Small Cube: Dimensions are \(4 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{side}^3 = 4^3 = 64 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 64 = 206 \, \text{in}^3
\]
Answer for Problem 2: \(\boxed{206 \, \text{in}^3}\)
---
The compound shape consists of two rectangular prisms placed side by side.
- Left Prism: Dimensions are \(8 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 2 \times 4 = 64 \, \text{in}^3 \).
- Right Prism: Dimensions are \(6 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 6 \times 2 \times 4 = 48 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 64 + 48 = 112 \, \text{in}^3
\]
Answer for Problem 3: \(\boxed{112 \, \text{in}^3}\)
---
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 4 = 32 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 32 = 238 \, \text{in}^3
\]
Answer for Problem 4: \(\boxed{238 \, \text{in}^3}\)
---
The compound shape consists of two rectangular prisms stacked on top of each other.
- Top Prism: Dimensions are \(5 \, \text{in} \times 5 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 5 \times 5 \times 5 = 125 \, \text{in}^3 \).
- Bottom Prism: Dimensions are \(8 \, \text{in} \times 5 \, \text{in} \times 6 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 5 \times 6 = 240 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 125 + 240 = 365 \, \text{in}^3
\]
Answer for Problem 5: \(\boxed{365 \, \text{in}^3}\)
---
The compound shape consists of two rectangular prisms placed side by side.
- Left Prism: Dimensions are \(6 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 6 \times 4 \times 4 = 96 \, \text{in}^3 \).
- Right Prism: Dimensions are \(4 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 4 \times 4 = 64 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 96 + 64 = 160 \, \text{in}^3
\]
Answer for Problem 6: \(\boxed{160 \, \text{in}^3}\)
---
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 4 = 32 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 32 = 238 \, \text{in}^3
\]
Answer for Problem 7: \(\boxed{238 \, \text{in}^3}\)
---
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(7 \, \text{in} \times 5 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 7 \times 5 \times 5 = 175 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(3 \, \text{in} \times 2 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 3 \times 2 \times 5 = 30 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 175 - 30 = 145 \, \text{in}^3
\]
Answer for Problem 8: \(\boxed{145 \, \text{in}^3}\)
---
1. \(\boxed{264 \, \text{in}^3}\)
2. \(\boxed{206 \, \text{in}^3}\)
3. \(\boxed{112 \, \text{in}^3}\)
4. \(\boxed{238 \, \text{in}^3}\)
5. \(\boxed{365 \, \text{in}^3}\)
6. \(\boxed{160 \, \text{in}^3}\)
7. \(\boxed{238 \, \text{in}^3}\)
8. \(\boxed{145 \, \text{in}^3}\)
---
Problem 1:
The compound shape consists of two rectangular prisms stacked on top of each other.
- Top Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 3 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 3 = 24 \, \text{in}^3 \).
- Bottom Prism: Dimensions are \(8 \, \text{in} \times 5 \, \text{in} \times 6 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 5 \times 6 = 240 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 24 + 240 = 264 \, \text{in}^3
\]
Answer for Problem 1: \(\boxed{264 \, \text{in}^3}\)
---
Problem 2:
The compound shape consists of a rectangular prism with a smaller cube cut out from one corner.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Small Cube: Dimensions are \(4 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{side}^3 = 4^3 = 64 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 64 = 206 \, \text{in}^3
\]
Answer for Problem 2: \(\boxed{206 \, \text{in}^3}\)
---
Problem 3:
The compound shape consists of two rectangular prisms placed side by side.
- Left Prism: Dimensions are \(8 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 2 \times 4 = 64 \, \text{in}^3 \).
- Right Prism: Dimensions are \(6 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 6 \times 2 \times 4 = 48 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 64 + 48 = 112 \, \text{in}^3
\]
Answer for Problem 3: \(\boxed{112 \, \text{in}^3}\)
---
Problem 4:
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 4 = 32 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 32 = 238 \, \text{in}^3
\]
Answer for Problem 4: \(\boxed{238 \, \text{in}^3}\)
---
Problem 5:
The compound shape consists of two rectangular prisms stacked on top of each other.
- Top Prism: Dimensions are \(5 \, \text{in} \times 5 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 5 \times 5 \times 5 = 125 \, \text{in}^3 \).
- Bottom Prism: Dimensions are \(8 \, \text{in} \times 5 \, \text{in} \times 6 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 8 \times 5 \times 6 = 240 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 125 + 240 = 365 \, \text{in}^3
\]
Answer for Problem 5: \(\boxed{365 \, \text{in}^3}\)
---
Problem 6:
The compound shape consists of two rectangular prisms placed side by side.
- Left Prism: Dimensions are \(6 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 6 \times 4 \times 4 = 96 \, \text{in}^3 \).
- Right Prism: Dimensions are \(4 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 4 \times 4 = 64 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 96 + 64 = 160 \, \text{in}^3
\]
Answer for Problem 6: \(\boxed{160 \, \text{in}^3}\)
---
Problem 7:
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(10 \, \text{in} \times 3 \, \text{in} \times 9 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 9 = 270 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(4 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 4 = 32 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 270 - 32 = 238 \, \text{in}^3
\]
Answer for Problem 7: \(\boxed{238 \, \text{in}^3}\)
---
Problem 8:
The compound shape consists of a large rectangular prism with a smaller rectangular prism cut out from one side.
- Large Rectangular Prism: Dimensions are \(7 \, \text{in} \times 5 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 7 \times 5 \times 5 = 175 \, \text{in}^3 \).
- Cut-Out Rectangular Prism: Dimensions are \(3 \, \text{in} \times 2 \, \text{in} \times 5 \, \text{in}\).
- Volume = \( \text{length} \times \text{width} \times \text{height} = 3 \times 2 \times 5 = 30 \, \text{in}^3 \).
- Total Volume:
\[
\text{Total Volume} = 175 - 30 = 145 \, \text{in}^3
\]
Answer for Problem 8: \(\boxed{145 \, \text{in}^3}\)
---
Final Answers:
1. \(\boxed{264 \, \text{in}^3}\)
2. \(\boxed{206 \, \text{in}^3}\)
3. \(\boxed{112 \, \text{in}^3}\)
4. \(\boxed{238 \, \text{in}^3}\)
5. \(\boxed{365 \, \text{in}^3}\)
6. \(\boxed{160 \, \text{in}^3}\)
7. \(\boxed{238 \, \text{in}^3}\)
8. \(\boxed{145 \, \text{in}^3}\)
Parent Tip: Review the logic above to help your child master the concept of finding volume of irregular shapes worksheet.
