To solve this problem, we can break it down into a few steps:

1. Calculate the Volume of the Tank:

The tank's dimensions are given as $90 \, \text{cm} \times 50 \, \text{cm} \times 30 \, \text{cm}$.

$\text{Volume of the tank} = 90 \times 50 \times 30 \, \text{cm}^3 = 135,000 \, \text{cm}^3$

2. Calculate the Volume of Water Added:

Water is added at a rate of $8 \, \frac{1}{4}$ liters per minute for 16 minutes. First, convert $8 \, \frac{1}{4}$ liters to an improper fraction:

$8 \, \frac{1}{4} = \frac{33}{4} \, \text{liters per minute}$

The total volume of water added is:

$\text{Total water added} = \frac{33}{4} \times 16 \, \text{liters} = 132 \, \text{liters}$

Since 1 liter is equivalent to 1000 cm³:

$\text{Total water added in cm}^3 = 132 \times 1000 \, \text{cm}^3 = 132,000 \, \text{cm}^3$

3. Determine the Volume Occupied by the Cubes:

The total volume occupied by water and the cubes must equal the volume of the tank:

$\text{Volume of tank} = \text{Volume of water added} + \text{Volume of cubes}$

$135,000 \, \text{cm}^3 = 132,000 \, \text{cm}^3 + \text{Volume of cubes}$

$\text{Volume of cubes} = 135,000 \, \text{cm}^3 - 132,000 \, \text{cm}^3 = 3,000 \, \text{cm}^3$

4. Calculate the Edge of Each Cube:

Let the edge length of each cube be $x$ cm. The volume of one cube is $x^3$, and since there are 3 identical cubes:

$3x^3 = 3,000 \, \text{cm}^3$

$x^3 = \frac{3,000}{3} = 1,000 \, \text{cm}^3$

Taking the cube root of both sides:

$x = \sqrt[3]{1,000} = 10 \, \text{cm}$

Final Answer:

The edge of each cube is 10 cm.

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Do you want more details or have any questions about the solution?

Here are some related questions for practice:

1. If the tank had only two cubes, how long would it take to fill?
2. How much water would be required if the cubes were twice as large?
3. If the water flow rate was doubled, how long would it take to fill the tank?
4. What would the edge length be if the total cube volume was 8,000 cm³?
5. How much space would be left in the tank if no cubes were placed in it?

Tip: Always convert volumes and rates to consistent units before performing calculations.