The data shows volume and height of 4 right circular tanks P, Q, R and S. The given data also depicts time taken to fill or empty the tank by inlet pipe A, B and outlet pipe C.

1. Ratio between time taken by pipe B and that by pipe C is different because pipes were used by the operator in different ways for different tanks.
2. Radius of tank S is 10.5 m.

Tank	Volume	Height	Time taken by pipe A to fill tank (in hours)	Ratio of time taken by pipe B to fill and pipe C to empty the tank
P	38808	28	10	2: 3
Q	--------	10	12	3: 2
R	5390	35	18	1: 3
S	19250	--------	---------	2: 5

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

The correct answer is 14 m.

We can solve this problem step-by-step as follows:

Step 1: Determine the time taken by each pipe to fill or empty tank Q.
From the table, the time taken by inlet pipe A to fill tank Q is 12 hours.
We are given that pipe B alone can fill tank Q in 36 hours.
The ratio of time taken by pipe B to fill tank Q to that taken by pipe C to empty the tank is 3:2.

Let the time taken by pipe C to empty the tank be $T_C$ hours.

$\frac{36}{T_C}=\frac{3}{2}$

$\Rightarrow T_C=\frac{36\times 2}{3}=24\text{hours}$

So, outlet pipe C can empty the tank Q in 24 hours.

Step 2: Find the fraction of the tank filled in 1 hour when all three pipes are opened together.
Pipes A and B are inlet pipes (filling the tank), and C is an outlet pipe (emptying the tank). The net rate of filling in 1 hour is:

$\text{Net Rate}=\frac{1}{12}+\frac{1}{36}-\frac{1}{24}$

Taking the Least Common Multiple (LCM) of 12, 36, and 24, which is 72, we get:

$\text{Net Rate}=\frac{6+2-3}{72}=\frac{5}{72}$

Thus, in 1 hour, $\frac{5}{72}$ of the total volume of tank Q is filled.

Step 3: Calculate the total volume of tank Q.
We are given that when all three pipes were opened for 1 hour, the volume of tank Q filled was approximately 428 cubic meters.

Let $V$ be the total volume of tank Q.

$\frac{5}{72}\times V=428$

$\Rightarrow V=\frac{428\times 72}{5}=6163.2{\text{m}}^3$

Step 4: Find the approximate radius of tank Q.
The tank Q is a right circular cylinder with height $h=10\text{m}$ (from the table).
The volume $V$ of a cylinder is given by the formula:

$V=\pi r^{2}h$

Substituting the values of $V$, $h$, and $\pi \approx \frac{22}{7}$ into the formula:

$6163.2=\frac{22}{7}\times r^2\times 10$

$\Rightarrow r^2=\frac{6163.2\times 7}{220}$

$\Rightarrow r^2\approx 196.1$

$\Rightarrow r\approx \sqrt{196}=14\text{m}$

Therefore, the approximate radius of tank Q is 14 m.