Mathematically similar containers have volumes that scale with the cube of their corresponding linear dimensions (such as height).

Step 1: Establish the Scale Factor

The height ratio between the smaller and larger container is:

$\frac{30}{75} = \frac{2}{5}$

Since volume scales with the cube of the linear ratio:

$\text{Volume scale factor} = \left(\frac{2}{5}\right)^3 = \frac{8}{125}$

Step 2: Calculate the Volume of the Smaller Container

The larger container has a capacity of 5.5 litres = 5500 millilitres.

$\text{Smaller container volume} = 5500 \times \frac{8}{125}$

$= 5500 \times 0.064$

$= 352 \text{ mL}$

Final Answer:

The capacity of the smaller container is 352 mL.

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Do you want a more detailed breakdown or have any questions?

Here are some related questions:

1. How do you find the ratio of two mathematically similar objects?
2. Why does volume scale with the cube of the linear ratio?
3. How do you convert between litres and millilitres?
4. What other real-world applications use volume scaling?
5. How does surface area scale for mathematically similar objects?

Tip: When working with similar shapes, always determine whether you're dealing with length, area, or volume before applying the ratio. 🚀