Let's go through this problem step by step.

1. Calculate the Volume of the Fish Tank:

   • The tank is in the shape of a cuboid with dimensions: $\text{Length} = 100 \text{ cm}, \quad \text{Width} = 30 \text{ cm}, \quad \text{Height} = 30 \text{ cm}$
   • The volume $V$ of a cuboid is given by: $V = \text{Length} \times \text{Width} \times \text{Height}$
   • Substituting the given values: $V = 100 \times 30 \times 30 = 90000 \text{ cm}^3$

2. Convert Volume from Cubic Centimeters to Liters:

   • We know that $1000 \text{ cm}^3 = 1 \text{ liter}$.
   • So, the volume in liters is: $\frac{90000 \text{ cm}^3}{1000} = 90 \text{ liters}$

3. Convert Liters to Gallons:

   • Given $4.5 \text{ liters} = 1 \text{ gallon}$, we convert 90 liters to gallons: $\frac{90}{4.5} = 20 \text{ gallons}$

4. Calculate the Number of Fish the Tank Can Hold:

   • According to the problem, for every gallon of water, Sam can keep 2 small fish.
   • So, for 20 gallons, the number of fish Sam can keep is: $20 \times 2 = 40 \text{ fish}$

5. Conclusion:

   • Sam thinks he can keep 36 fish, but the tank can actually hold up to 40 fish based on the water volume and the given rule.

Therefore, Sam is correct in thinking he can keep 36 fish, as this number is within the tank's capacity.

Would you like more details on any of these steps, or do you have any questions?

Here are some additional questions to deepen understanding:

1. How would the fish capacity change if the tank dimensions were increased by 10 cm in each direction?
2. What would be the new fish capacity if Sam changed his rule to 3 fish per gallon?
3. How does the tank's capacity change if filled only halfway?
4. If a larger tank held 150 liters, how many fish could it accommodate with Sam's rule?
5. What if Sam wanted to keep 50 fish in this tank—how much extra water would he need?

Tip: When working with volume conversions, always double-check units and conversion factors for accuracy.