Determine the volume scale factor for similar 3D shapes given their volumes or linear dimensions.

Let $V_1 = 324 \text{ cm}^3$ and $V_2 = 96 \text{ cm}^3$.

The volume scale factor is the ratio of the volumes.

The volume scale factor is $\boxed{\frac{27}{8}}$.

2. A scouts tent in the shape of a triangular prism has a cross-sectional area of $10 \text{ m}^2$ and a length of $5 \text{ m}$. Another similar tent has a cross-sectional area of $40 \text{ m}^2$ and length $10 \text{ m}$. Determine the volume scale factor.

For Tent 1: $L_1 = 5 \text{ m}$.
For Tent 2: $L_2 = 10 \text{ m}$.

The linear scale factor is the ratio of corresponding lengths.

The volume scale factor is the cube of the linear scale factor ($k^3$).

The volume scale factor is $\boxed{8}$.

3. A model of a cylindrical water tank has a radius of $10.5 \text{ cm}$ and a height of $15 \text{ cm}$. Its actual radius is $210 \text{ cm}$. Determine:
a. the volume of the actual water tank. (Take $\pi = 3.142$)
b. the volume scale factor.

a) The volume of the actual water tank.

Model: $r_m = 10.5 \text{ cm}$, $h_m = 15 \text{ cm}$.
Actual: $r_a =