To solve this problem, we first need to understand how the volume ratio relates to the given side length ratio.

Step 1: Understanding the side length ratio

The ratio of side lengths between the cuboid on the left and the cuboid on the right is $2:3$. This means that for each corresponding dimension (length, width, height), the side length of the cuboid on the right is $\frac{3}{2}$ times the side length of the cuboid on the left.

Step 2: Relating the side length ratio to the volume ratio

Since volume is calculated as the product of the length, width, and height ($V = l \times w \times h$), the volume ratio will be the cube of the side length ratio: $\text{Volume ratio} = \left( \frac{3}{2} \right)^3 = \frac{27}{8}$

Step 3: Calculating the volume of the cuboid on the right

Given that the volume of the cuboid on the left is 192 cm³, we can find the volume of the cuboid on the right by multiplying 192 by the volume ratio: $\text{Volume of the cuboid on the right} = 192 \times \frac{27}{8} = 192 \times 3.375 = 648 \text{ cm}^3$

Thus, the volume of the cuboid on the right is 648 cm³.

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Would you like further details or have any questions?

Here are 5 related questions:

1. What would the volume of the cuboid be if the side length ratio was 1:2?
2. How would the volume change if the side length ratio was reversed (3:2)?
3. If the volume of the cuboid on the right was given, how would you find the volume of the cuboid on the left?
4. How does changing just one dimension (e.g., length) affect the volume ratio?
5. How does the concept of ratios apply to other geometric shapes like spheres or cylinders?

Tip: When dealing with ratios involving volume, remember that the change affects all three dimensions, so the volume ratio will be the cube of the side length ratio.