Pipe B alone can fill the tank Q in 36 hours. When all three pipes were opened for 1 hour, the volume of tank Q filled was approximately 428 cubic meters. What is the approximate radius of tank Q?

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**Solution:**

1. Given that pipe B alone fills tank Q in 36 hours.

2. Time taken by pipe B to fill $ \frac{2}{3} $ of tank Q is:
   $$
   36 \times \frac{2}{3} = 24 \text{ hours}
   $$

3. Let the capacity of tank Q be 72 units (chosen for ease of calculation).

4. Efficiency (filling rate) of pipes A, B, and C are given as 6, 2, and 3 units per hour respectively.

5. When all three pipes are opened for 1 hour, the volume filled is:
   $$
   (6 + 2 - 3) = 5 \text{ units}
   $$

6. The volume filled in 1 hour is approximately 428 cubic meters, so 1 unit corresponds to:
   $$
   \frac{428}{5} = 85.6 \text{ cubic meters}
   $$

7. Total capacity of tank Q in cubic meters is:
   $$
   72 \times 85.6 = 6163.2 \text{ cubic meters}
   $$

8. Assuming the tank is cylindrical with height $ h = 10 $ meters, volume $ V $ is:
   $$
   V = \pi r^2 h
   $$

9. Rearranging for radius $ r $:
   $$
   r = \sqrt{\frac{V}{\pi h}}
   $$

10. Substitute values:
    $$
    r = \sqrt{\frac{6163.2}{\frac{22}{7} \times 10}} = \sqrt{\frac{6163.2 \times 7}{22 \times 10}} = \sqrt{196.08} \approx 14 \text{ meters}
    $$

**Answer:** 14 m

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