14. A rectangular tank with a base measuring 50 cm by 24 cm contained 3.6 of water. When 74 identical marbles were dropped into the tank, me water level rose 10 a certain height. If 26 marbles were removed from the tank, the new water level became 9 cm . Find the volume of each marble.

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To solve the problem, we need to follow these steps:

1. **Extract known conditions:**
   - The base dimensions of the tank are $$50 \, \text{cm} \times 24 \, \text{cm}$$.
   - The initial water level is $$3.6 \, \text{cm}$$.
   - When $$74$$ marbles are added, the water level rises by a certain height.
   - After removing $$26$$ marbles, the new water level is $$9 \, \text{cm}$$.

2. **Calculate the initial volume of water in the tank:**
   The volume of water can be calculated using the formula for the volume of a rectangular prism:
   $$
   V = \text{base area} \times \text{height}
   $$
   The base area $$A$$ is:
   $$
   A = 50 \times 24
   $$
   The initial height of the water is $$3.6 \, \text{cm}$$.

3. **Calculate the new water level after adding marbles:**
   Let $$h$$ be the height the water level rises when $$74$$ marbles are added. The new height after adding the marbles is:
   $$
   3.6 + h
   $$

4. **Calculate the volume of water after removing marbles:**
   After removing $$26$$ marbles, the number of marbles left is $$74 - 26 = 48$$. The new water level is $$9 \, \text{cm}$$.

5. **Set up the equations:**
   The volume of water after adding $$74$$ marbles is equal to the volume of water after removing $$26$$ marbles:
   $$
   \text{Volume after adding marbles} = \text{Volume after removing marbles}
   $$

6. **Calculate the volume of each marble:**
   The volume displaced by the marbles can be calculated using the change in water level.

Now, let's perform the calculations step by step.

### Step 1: Calculate the initial volume of water
$$
A = 50 \times 24 = 1200 \, \text{cm}^2
$$
$$
V_{\text{initial}} = 1200 \times 3.6
$$

### Step 2: Calculate the new volume after removing marbles
The new height is $$9 \, \text{cm}$$:
$$
V_{\text{new}} = 1200 \times 9
$$

### Step 3: Set up the equations
The volume of water displaced by the marbles can be calculated as:
$$
V_{\text{displaced}} = V_{\text{new}} - V_{\text{initial}}
$$

### Step 4: Calculate the volume of each marble
Let $$v$$ be the volume of each marble. The volume displaced by $$74$$ marbles is:
$$
74v = V_{\text{displaced}}
$$

Now, let's calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$1200\times 3.6$$
- step1: Multiply the numbers:
  $$4320$$
Calculate or simplify the expression $$ 1200 * 9 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1200\times 9$$
- step1: Multiply the numbers:
  $$10800$$
Calculate or simplify the expression $$ 10800 - 4320 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10800-4320$$
- step1: Subtract the numbers:
  $$6480$$
Calculate or simplify the expression $$ 6480 / 74 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{6480}{74}$$
- step1: Reduce the fraction:
  $$\frac{3240}{37}$$
Now that we have completed the calculations, let's summarize the results:

1. **Initial volume of water in the tank:**
   $$
   V_{\text{initial}} = 4320 \, \text{cm}^3
   $$

2. **Volume of water after removing marbles:**
   $$
   V_{\text{new}} = 10800 \, \text{cm}^3
   $$

3. **Volume displaced by the marbles:**
   $$
   V_{\text{displaced}} = V_{\text{new}} - V_{\text{initial}} = 10800 - 4320 = 6480 \, \text{cm}^3
   $$

4. **Volume of each marble:**
   The volume displaced by $$74$$ marbles is equal to the volume of the marbles:
   $$
   74v = 6480
   $$
   Therefore, the volume of each marble $$v$$ is:
   $$
   v = \frac{6480}{74} \approx 87.56 \, \text{cm}^3
   $$

Thus, the volume of each marble is approximately $$87.56 \, \text{cm}^3$$.
Each marble has a volume of approximately $$87.56 \, \text{cm}^3$$.

A rectangular tank with a base measuring 50 cm by 24 cm contained
3.6 of water. When 74 identical marbles were dropped into the tank,
me water level rose 10 a certain height. If 26 marbles were removed
from the tank, the new water level became 9 cm . Find the volume of
each marble.

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