Educational worksheet for calculating volume and surface area of cuboids and cubes, featuring diagrams and measurement data.

To solve the problems in the worksheet, we need to calculate the volume and surface area for each cuboid and cube. Let's go through each section step by step.

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Section A: Cuboids

#### Formulae for Cuboids:
1. Volume: \( V = \text{length} \times \text{width} \times \text{height} \)
2. Surface Area: \( SA = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length}) \)

#### Cuboid 1:
- Dimensions: \( 3 \, \text{cm} \times 2 \, \text{cm} \times 5 \, \text{cm} \)
- Volume:
\[
V = 3 \times 2 \times 5 = 30 \, \text{cm}^3
\]
- Surface Area:
\[
SA = 2(3 \times 2 + 2 \times 5 + 5 \times 3) = 2(6 + 10 + 15) = 2 \times 31 = 62 \, \text{cm}^2
\]

#### Cuboid 2:
- Dimensions: \( 9 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} \)
- Volume:
\[
V = 9 \times 3 \times 2 = 54 \, \text{cm}^3
\]
- Surface Area:
\[
SA = 2(9 \times 3 + 3 \times 2 + 2 \times 9) = 2(27 + 6 + 18) = 2 \times 51 = 102 \, \text{cm}^2
\]

#### Cuboid 3:
- Dimensions: \( 4 \, \text{m} \times 4 \, \text{m} \times 12 \, \text{m} \)
- Volume:
\[
V = 4 \times 4 \times 12 = 192 \, \text{m}^3
\]
- Surface Area:
\[
SA = 2(4 \times 4 + 4 \times 12 + 12 \times 4) = 2(16 + 48 + 48) = 2 \times 112 = 224 \, \text{m}^2
\]

#### Cuboid 4:
- Dimensions: \( 110 \, \text{mm} \times 20 \, \text{mm} \times 70 \, \text{mm} \)
- Volume:
\[
V = 110 \times 20 \times 70 = 154,000 \, \text{mm}^3
\]
- Surface Area:
\[
SA = 2(110 \times 20 + 20 \times 70 + 70 \times 110) = 2(2200 + 1400 + 7700) = 2 \times 11300 = 22,600 \, \text{mm}^2
\]

---

Section B: Cubes

#### Formulae for Cubes:
1. Volume: \( V = \text{side}^3 \)
2. Surface Area: \( SA = 6 \times \text{side}^2 \)

#### Cube 1:
- Side length: \( 6 \, \text{cm} \)
- Volume:
\[
V = 6^3 = 216 \, \text{cm}^3
\]
- Surface Area:
\[
SA = 6 \times 6^2 = 6 \times 36 = 216 \, \text{cm}^2
\]

#### Cube 2:
- Side length: \( 30 \, \text{mm} \)
- Volume:
\[
V = 30^3 = 27,000 \, \text{mm}^3
\]
- Surface Area:
\[
SA = 6 \times 30^2 = 6 \times 900 = 5,400 \, \text{mm}^2
\]

#### Cube 3:
- Side length: \( 8 \, \text{m} \)
- Volume:
\[
V = 8^3 = 512 \, \text{m}^3
\]
- Surface Area:
\[
SA = 6 \times 8^2 = 6 \times 64 = 384 \, \text{m}^2
\]

#### Cube 4:
- Side length: \( 5 \, \text{cm} \)
- Volume:
\[
V = 5^3 = 125 \, \text{cm}^3
\]
- Surface Area:
\[
SA = 6 \times 5^2 = 6 \times 25 = 150 \, \text{cm}^2
\]

---

Final Answers:

#### Cuboids:
1. \( 30 \, \text{cm}^3 \), \( 62 \, \text{cm}^2 \)
2. \( 54 \, \text{cm}^3 \), \( 102 \, \text{cm}^2 \)
3. \( 192 \, \text{m}^3 \), \( 224 \, \text{m}^2 \)
4. \( 154,000 \, \text{mm}^3 \), \( 22,600 \, \text{mm}^2 \)

#### Cubes:
1. \( 216 \, \text{cm}^3 \), \( 216 \, \text{cm}^2 \)
2. \( 27,000 \, \text{mm}^3 \), \( 5,400 \, \text{mm}^2 \)
3. \( 512 \, \text{m}^3 \), \( 384 \, \text{m}^2 \)
4. \( 125 \, \text{cm}^3 \), \( 150 \, \text{cm}^2 \)

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{c|c|c}
\text{Cuboid} & \text{Volume} & \text{Surface Area} \\
\hline
1 & 30 \, \text{cm}^3 & 62 \, \text{cm}^2 \\
2 & 54 \, \text{cm}^3 & 102 \, \text{cm}^2 \\
3 & 192 \, \text{m}^3 & 224 \, \text{m}^2 \\
4 & 154,000 \, \text{mm}^3 & 22,600 \, \text{mm}^2 \\
\hline
\text{Cube} & \text{Volume} & \text{Surface Area} \\
\hline
1 & 216 \, \text{cm}^3 & 216 \, \text{cm}^2 \\
2 & 27,000 \, \text{mm}^3 & 5,400 \, \text{mm}^2 \\
3 & 512 \, \text{m}^3 & 384 \, \text{m}^2 \\
4 & 125 \, \text{cm}^3 & 150 \, \text{cm}^2 \\
\end{array}
}
\]