To solve this problem, we need to calculate the volume of one cylindrical cup and determine how many cups are required for a given volume of liquid.

Given:

• The diameter of the cup is 6 cm, hence the radius $r$ is $3$ cm ($\frac{6}{2}$).
• The height $h$ of the cup is 9 cm.

The formula for the volume $V$ of a cylinder is: $V = \pi r^2 h$

Now, substituting the given values: $V = \pi \times (3 \, \text{cm})^2 \times 9 \, \text{cm}$ $V = \pi \times 9 \, \text{cm}^2 \times 9 \, \text{cm}$ $V = 81\pi \, \text{cm}^3$

Thus, the volume of one cup is $81\pi \, \text{cm}^3$.

However, to determine the number of cups needed, we need to know the total volume of water that is required. Without this information, we cannot calculate the exact number of cups needed.

If you provide the total volume of water that needs to be served, we can proceed with the calculation.

Do you want more details or have any questions about the calculations so far?

Here are 8 related questions to expand on this topic:

1. What is the total volume of water that needs to be served?
2. How would you calculate the volume of a cylindrical object in general?
3. Can you find the surface area of the cylinder given the same dimensions?
4. What is the relationship between the diameter and the radius of a cylinder?
5. How does the height of a cylinder affect its volume?
6. If the radius of the cylinder was doubled, how would that affect the volume?
7. How can you convert the volume from cubic centimeters to liters?
8. How would the calculations change if the cup were a different shape, such as a cone?

Tip: Always double-check your calculations and ensure you are using the correct units.