This question involves two mathematically similar boats, where the smaller boat has a height of 5 cm and a volume of 60 cm³, while the larger boat has a height of 20 cm. The task is to find the volume of the larger boat.

Since the boats are similar, the ratio of their corresponding lengths is proportional, and their volumes are proportional to the cube of the scale factor.

Steps:

1. Find the scale factor for the height: $\text{Scale factor} = \frac{\text{Height of larger boat}}{\text{Height of smaller boat}} = \frac{20}{5} = 4$

2. Apply the cube of the scale factor to the volume: Since volume scales with the cube of the linear dimensions: $\text{Scale factor for volume} = 4^3 = 64$

3. Calculate the volume of the larger boat: $\text{Volume of larger boat} = 60 \, \text{cm}^3 \times 64 = 3840 \, \text{cm}^3$

Thus, the volume of the larger boat is 3840 cm³.

Would you like further details or have any questions?

Related questions:

1. What is the general relationship between dimensions and volume for similar shapes?
2. How does the cube of a scale factor affect surface area?
3. Can the same principle be applied to three-dimensional shapes like spheres?
4. What happens to the surface area if the scale factor for height is doubled?
5. How can we use this concept in real-life applications, like modeling?

Tip: Always remember that when dealing with similar objects, volumes scale with the cube of the linear scale factor.