Solution:

The problem involves similar shapes, meaning their corresponding sides are proportional. The ratio of the sides is the same as the ratio of their perimeters.

Step 1: Determine the scale factor

• Height of shape $Q = 3 \, \text{cm}$
• Height of shape $R = 30 \, \text{cm}$

The scale factor is: $\text{Scale factor} = \frac{\text{Height of R}}{\text{Height of Q}} = \frac{30}{3} = 10$

Step 2: Use the scale factor to calculate the perimeter

• Perimeter of $Q = 18 \, \text{cm}$

Since the shapes are similar: $\text{Perimeter of R} = \text{Scale factor} \times \text{Perimeter of Q} = 10 \times 18 = 180 \, \text{cm}$

Final Answer:

The perimeter of shape $R$ is: $\boxed{180 \, \text{cm}}$

Let me know if you need a detailed explanation or further clarifications!

Related Questions:

1. How do you verify the proportionality between two similar shapes?
2. If the scale factor changes, how does it affect the perimeter?
3. What is the relationship between areas of similar shapes?
4. Can the perimeter alone determine if two shapes are similar?
5. How is the scale factor applied in real-life geometric problems?

Tip:

When working with similar shapes, always identify and compare corresponding sides or heights to find the scale factor before applying it to other properties like perimeter or area.