Find the surface area of the sphere.

Given:
Radius ($r$) = $42 \text{ cm}$
Formula for surface area ($SA$) = $4\pi r^2$
Use $\pi = \frac{22}{7}$.
The final answer must be in square meters. First, convert the radius to meters:

$$r = 42 \text{ cm} = 0.42 \text{ m}$$

Substitute the values into the formula:

$$SA = 4 \times \frac{22}{7} \times (0.42 \text{ m})^2$$ $$SA = \frac{88}{7} \times 0.1764 \text{ m}^2$$ $$SA = 12.5714... \times 0.1764 \text{ m}^2$$ $$SA = 2.2176 \text{ m}^2$$ $$\boxed{2.2176 \text{ m}^2}$$

Given:
Radius ($r$) = $10 \text{ cm}$
Height ($h$) = $30 \text{ cm}$
Formula for volume ($V$) = $\frac{1}{3}\pi r^2 h$
Use $\pi = 3.14$.
Substitute the values into the formula:

$$V = \frac{1}{3} \times 3.14 \times (10 \text{ cm})^2 \times 30 \text{ cm}$$ $$V = \frac{1}{3} \times 3.14 \times 100 \text{ cm}^2 \times 30 \text{ cm}$$ $$V = 3.14 \times 100 \text{ cm}^2 \times \frac{30}{3} \text{ cm}$$ $$V = 3.14 \times 100 \text{ cm}^2 \times 10 \text{ cm}$$ $$V = 3.14 \times 1000 \text{ cm}^3$$ $$V = 3140 \text{ cm}^3$$ $$\boxed{3140 \text{ cm}^3}$$

Given:
Side length ($s$) = $6\sqrt{2} \text{ cm}$
The formula for the volume of a cube is $V = s^3$.
Substitute the side length into the formula:

$$V = (6\sqrt{2} \text{ cm})^3$$ $$V = 6^3 \times (\sqrt{2})^3 \text{ cm}^3$$ $$V = (6 \times 6 \times 6) \times (\sqrt{2} \times \sqrt{2} \times \sqrt{2}) \text{ cm}^3$$ $$V = 216 \times (2 \times \sqrt{2}) \text{ cm}^3$$ $$V = 216 \times 2\sqrt{2} \text{ cm}^3$$ $$V = 432\sqrt{2} \text{ cm}^3$$ $$\boxed{432\sqrt{2} \text{ cm}^3}$$