To find the height of the scale model in centimeters, we need to use the given scale relationship between centimeters and meters. The scale tells us that 3 centimeters represents 45 meters. We can set up a proportion to solve for the height of the scale model.

First, we establish the proportion based on the given scale:

$\frac{3 \text{ cm}}{45 \text{ m}} = \frac{x \text{ cm}}{360 \text{ m}}$

Here, $x$ represents the height of the scale model in centimeters. Now we solve for $x$ by cross-multiplying:

$3 \text{ cm} \times 360 \text{ m} = 45 \text{ m} \times x \text{ cm}$

$1080 \text{ cm} \cdot \text{m} = 45 \text{ m} \cdot x \text{ cm}$

Next, we isolate $x$ by dividing both sides of the equation by 45:

$x = \frac{1080 \text{ cm} \cdot \text{m}}{45 \text{ m}}$

$x = 24 \text{ cm}$

Therefore, the height of the scale model is $24$ centimeters.

Would you like any details or have any questions about this solution?

Here are 5 relative questions that expand upon this information:

1. If the scale model was built using a scale of 1 cm to 20 m, what would be the new height of the model?
2. How would you convert the scale ratio from 3 cm:45 m to a unit-less ratio?
3. What is the actual height in meters of a model that is 10 cm tall using the given scale?
4. If the artist decides to double the height of the scale model, what would the new height be in centimeters?
5. How would the scale change if the artist wanted each centimeter to represent 30 meters instead?

Tip: When working with scales, always ensure the units are consistent before setting up your proportion to avoid calculation errors.