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We are tasked with determining the volume of water poured out of Tank A and distributed between Tanks B and C, such that the heights of water in all the tanks are equal. Here's how we can approach the problem:

### Step 1: Volume of water in Tank A (initial volume)

Tank A has dimensions:
- Height = 11 cm
- Length = 12 cm
- Width = 10 cm

The volume of water in Tank A is given by the formula for the volume of a rectangular prism:
\[
V_A = \text{Length} \times \text{Width} \times \text{Height} = 12 \, \text{cm} \times 10 \, \text{cm} \times 11 \, \text{cm} = 1320 \, \text{cm}^3
\]

### Step 2: Set up for equal water heights in all tanks

The height of the water in Tanks A, B, and C will be the same after pouring, so let the common height of the water be \( h \, \text{cm} \).

Tank B has dimensions:
- Length = 10 cm
- Width = 7 cm
- Height of water = \( h \)

The volume of water in Tank B:
\[
V_B = 10 \, \text{cm} \times 7 \, \text{cm} \times h = 70h \, \text{cm}^3
\]

Tank C has dimensions:
- Length = 6 cm
- Width = 5 cm
- Height of water = \( h \)

The volume of water in Tank C:
\[
V_C = 6 \, \text{cm} \times 5 \, \text{cm} \times h = 30h \, \text{cm}^3
\]

Tank A will also retain some water, so the remaining volume in Tank A is:
\[
V'_A = 12 \, \text{cm} \times 10 \, \text{cm} \times h = 120h \, \text{cm}^3
\]

### Step 3: Conservation of volume

The total volume of water is conserved, so:
\[
V_A = V'_A + V_B + V_C
\]

Substituting the known expressions for volume:
\[
1320 = 120h + 70h + 30h
\]

Simplifying:
\[
1320 = 220h
\]

### Step 4: Solve for \( h \)

\[
h = \frac{1320}{220} = 6 \, \text{cm}
\]

### Step 5: Calculate the volume poured out

The volume of water that remains in Tank A is:
\[
V'_A = 120 \times 6 = 720 \, \text{cm}^3
\]

Therefore, the volume of water poured out is:
\[
V_{\text{poured}} = 1320 - 720 = 600 \, \text{cm}^3
\]

Thus, the volume of water poured out of Tank A is **600 cm³**.

Would you like further details on any step or have any questions?

### Related Questions:
1. How would the problem change if the height of water in all tanks was 7 cm instead of 6 cm?
2. What would the volume be if Tank C had a different width or length?
3. How can we verify the water height \( h \) in different shapes, such as cylindrical tanks?
4. How does changing the size of one of the tanks affect the final water height?
5. Can this method be extended to more than two tanks?

### Tip:
Always ensure that the volume is conserved in problems involving fluid transfer, and set up an equation for total volume to solve for unknowns like water height.

Tank A is filled with water to a height of 11 cm. The water in Tank A is then poured into 2 empty rectangular tanks, B and C, such that the heights of water in all the tanks are equal. Find the volume of water poured out of tank A.

Solve the problem of finding the volume of water poured out of Tank A into Tanks B and C with equal water heights. Learn how to apply the formula for the volume of rectangular prisms and conservation of volume in this step-by-step solution.

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