The problem states:

• The dimensions of a rectangular aquarium are:
  • Length = 1.20 m (120 cm)
  • Width = 90 cm
• The aquarium is full of water.
• When 270 liters (270,000 cm³) of water is removed, the aquarium becomes $\frac{3}{4}$ full.
• We need to find the height of the water level when the aquarium is $\frac{3}{4}$ full.

Step-by-Step Solution:

1. Calculate the volume of the full aquarium: The volume $V$ of a rectangular aquarium is given by: $V = \text{length} \times \text{width} \times \text{height}$ Let $h$ be the height of the aquarium (when full). So, the volume when full is:

   = 10,800 \, \text{cm}^2 \times h$$

2. Relating the removed water to the volume change: If 270 liters (270,000 cm³) of water is removed, the aquarium becomes $\frac{3}{4}$ full. So, when full, the volume of water would be 4/4, and after removing the 270 liters, it becomes 3/4 full.

   Let the total volume when full be $V_{\text{full}}$. Then: $V_{\text{full}} - 270,000 \, \text{cm}^3 = \frac{3}{4} \times V_{\text{full}}$

3. Set up the equation: Substituting into the above equation: $V_{\text{full}} - 270,000 = \frac{3}{4} V_{\text{full}}$ Simplifying: $V_{\text{full}} - \frac{3}{4} V_{\text{full}} = 270,000$ $\frac{1}{4} V_{\text{full}} = 270,000$ $V_{\text{full}} = 270,000 \times 4 = 1,080,000 \, \text{cm}^3$

4. Find the height of the aquarium: Now that we know the total volume when full, we can use the formula for the volume: $1,080,000 = 120 \times 90 \times h$ Solving for $h$: $h = \frac{1,080,000}{120 \times 90} = \frac{1,080,000}{10,800} = 100 \, \text{cm}$

So, the height of the aquarium when full is 100 cm.

5. Find the height when the aquarium is $\frac{3}{4}$ full: When the aquarium is $\frac{3}{4}$ full, the height of the water will be: $h_{\frac{3}{4}} = \frac{3}{4} \times 100 = 75 \, \text{cm}$

Thus, the height of the water level when the aquarium is $\frac{3}{4}$ full is 75 cm.

Would you like any further details or explanations on the solution? Here are some related questions you might consider:

1. What would be the height of the water if half of it were removed?
2. How much water can the aquarium hold in liters when completely full?
3. If only 135 liters were removed, what fraction of the aquarium would still be full?
4. What is the surface area of the top of the water in the aquarium?
5. How much more water is needed to fill the aquarium back to its full height?

Tip: When dealing with volume problems, always ensure that the units are consistent. In this problem, we converted liters to cubic centimeters for accuracy.