Calculate the volume of each cube using the formula: volume = side × side × side.
A worksheet with six cubes, each labeled with side lengths, asking students to calculate the volume of each cube.
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Show Answer Key & Explanations
Step-by-step solution for: Volume of Solids Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Volume of Solids Worksheets
To solve the problem, we need to calculate the volume and surface area of each 3D shape shown in the image. Let's go through each shape step by step.
---
#### Dimensions:
- Side length = 6 units
#### Volume:
The formula for the volume of a cube is:
\[
V = \text{side}^3
\]
\[
V = 6^3 = 6 \times 6 \times 6 = 216 \text{ cubic units}
\]
#### Surface Area:
The formula for the surface area of a cube is:
\[
A = 6 \times (\text{side})^2
\]
\[
A = 6 \times 6^2 = 6 \times 36 = 216 \text{ square units}
\]
#### Answers:
- Volume: \( 216 \)
- Surface Area: \( 216 \)
---
#### Dimensions:
- Length = 8 units
- Width = 4 units
- Height = 4 units
#### Volume:
The formula for the volume of a rectangular prism is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 8 \times 4 \times 4 = 128 \text{ cubic units}
\]
#### Surface Area:
The formula for the surface area of a rectangular prism is:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(8 \times 4 + 4 \times 4 + 4 \times 8)
\]
\[
A = 2(32 + 16 + 32)
\]
\[
A = 2 \times 80 = 160 \text{ square units}
\]
#### Answers:
- Volume: \( 128 \)
- Surface Area: \( 160 \)
---
#### Dimensions:
- Length = 25 units
- Width = 20 units
- Height = 20 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 25 \times 20 \times 20 = 10000 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(25 \times 20 + 20 \times 20 + 20 \times 25)
\]
\[
A = 2(500 + 400 + 500)
\]
\[
A = 2 \times 1400 = 2800 \text{ square units}
\]
#### Answers:
- Volume: \( 10000 \)
- Surface Area: \( 2800 \)
---
#### Dimensions:
- Length = 21 units
- Width = 12 units
- Height = 12 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 21 \times 12 \times 12 = 3024 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(21 \times 12 + 12 \times 12 + 12 \times 21)
\]
\[
A = 2(252 + 144 + 252)
\]
\[
A = 2 \times 648 = 1296 \text{ square units}
\]
#### Answers:
- Volume: \( 3024 \)
- Surface Area: \( 1296 \)
---
#### Dimensions:
- Length = 7 units
- Width = 2 units
- Height = 2 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 7 \times 2 \times 2 = 28 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(7 \times 2 + 2 \times 2 + 2 \times 7)
\]
\[
A = 2(14 + 4 + 14)
\]
\[
A = 2 \times 32 = 64 \text{ square units}
\]
#### Answers:
- Volume: \( 28 \)
- Surface Area: \( 64 \)
---
#### Dimensions:
- Length = 8 units
- Width = 8 units
- Height = 1 unit
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 8 \times 8 \times 1 = 64 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(8 \times 8 + 8 \times 1 + 1 \times 8)
\]
\[
A = 2(64 + 8 + 8)
\]
\[
A = 2 \times 80 = 160 \text{ square units}
\]
#### Answers:
- Volume: \( 64 \)
- Surface Area: \( 160 \)
---
1. Volume: \( 216 \), Surface Area: \( 216 \)
2. Volume: \( 128 \), Surface Area: \( 160 \)
3. Volume: \( 10000 \), Surface Area: \( 2800 \)
4. Volume: \( 3024 \), Surface Area: \( 1296 \)
5. Volume: \( 28 \), Surface Area: \( 64 \)
6. Volume: \( 64 \), Surface Area: \( 160 \)
\boxed{
\begin{array}{ll}
1. & \text{Volume: } 216, \text{ Surface Area: } 216 \\
2. & \text{Volume: } 128, \text{ Surface Area: } 160 \\
3. & \text{Volume: } 10000, \text{ Surface Area: } 2800 \\
4. & \text{Volume: } 3024, \text{ Surface Area: } 1296 \\
5. & \text{Volume: } 28, \text{ Surface Area: } 64 \\
6. & \text{Volume: } 64, \text{ Surface Area: } 160 \\
\end{array}
}
---
1. Cube
#### Dimensions:
- Side length = 6 units
#### Volume:
The formula for the volume of a cube is:
\[
V = \text{side}^3
\]
\[
V = 6^3 = 6 \times 6 \times 6 = 216 \text{ cubic units}
\]
#### Surface Area:
The formula for the surface area of a cube is:
\[
A = 6 \times (\text{side})^2
\]
\[
A = 6 \times 6^2 = 6 \times 36 = 216 \text{ square units}
\]
#### Answers:
- Volume: \( 216 \)
- Surface Area: \( 216 \)
---
2. Rectangular Prism
#### Dimensions:
- Length = 8 units
- Width = 4 units
- Height = 4 units
#### Volume:
The formula for the volume of a rectangular prism is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 8 \times 4 \times 4 = 128 \text{ cubic units}
\]
#### Surface Area:
The formula for the surface area of a rectangular prism is:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(8 \times 4 + 4 \times 4 + 4 \times 8)
\]
\[
A = 2(32 + 16 + 32)
\]
\[
A = 2 \times 80 = 160 \text{ square units}
\]
#### Answers:
- Volume: \( 128 \)
- Surface Area: \( 160 \)
---
3. Rectangular Prism
#### Dimensions:
- Length = 25 units
- Width = 20 units
- Height = 20 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 25 \times 20 \times 20 = 10000 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(25 \times 20 + 20 \times 20 + 20 \times 25)
\]
\[
A = 2(500 + 400 + 500)
\]
\[
A = 2 \times 1400 = 2800 \text{ square units}
\]
#### Answers:
- Volume: \( 10000 \)
- Surface Area: \( 2800 \)
---
4. Rectangular Prism
#### Dimensions:
- Length = 21 units
- Width = 12 units
- Height = 12 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 21 \times 12 \times 12 = 3024 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(21 \times 12 + 12 \times 12 + 12 \times 21)
\]
\[
A = 2(252 + 144 + 252)
\]
\[
A = 2 \times 648 = 1296 \text{ square units}
\]
#### Answers:
- Volume: \( 3024 \)
- Surface Area: \( 1296 \)
---
5. Rectangular Prism
#### Dimensions:
- Length = 7 units
- Width = 2 units
- Height = 2 units
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 7 \times 2 \times 2 = 28 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(7 \times 2 + 2 \times 2 + 2 \times 7)
\]
\[
A = 2(14 + 4 + 14)
\]
\[
A = 2 \times 32 = 64 \text{ square units}
\]
#### Answers:
- Volume: \( 28 \)
- Surface Area: \( 64 \)
---
6. Rectangular Prism
#### Dimensions:
- Length = 8 units
- Width = 8 units
- Height = 1 unit
#### Volume:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = 8 \times 8 \times 1 = 64 \text{ cubic units}
\]
#### Surface Area:
\[
A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]
\[
A = 2(8 \times 8 + 8 \times 1 + 1 \times 8)
\]
\[
A = 2(64 + 8 + 8)
\]
\[
A = 2 \times 80 = 160 \text{ square units}
\]
#### Answers:
- Volume: \( 64 \)
- Surface Area: \( 160 \)
---
Final Answers:
1. Volume: \( 216 \), Surface Area: \( 216 \)
2. Volume: \( 128 \), Surface Area: \( 160 \)
3. Volume: \( 10000 \), Surface Area: \( 2800 \)
4. Volume: \( 3024 \), Surface Area: \( 1296 \)
5. Volume: \( 28 \), Surface Area: \( 64 \)
6. Volume: \( 64 \), Surface Area: \( 160 \)
\boxed{
\begin{array}{ll}
1. & \text{Volume: } 216, \text{ Surface Area: } 216 \\
2. & \text{Volume: } 128, \text{ Surface Area: } 160 \\
3. & \text{Volume: } 10000, \text{ Surface Area: } 2800 \\
4. & \text{Volume: } 3024, \text{ Surface Area: } 1296 \\
5. & \text{Volume: } 28, \text{ Surface Area: } 64 \\
6. & \text{Volume: } 64, \text{ Surface Area: } 160 \\
\end{array}
}
Parent Tip: Review the logic above to help your child master the concept of volume of solid figures worksheet.