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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.

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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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.

---

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.
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