Read the given below table carefully and answer the following questions

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

How much volume (approx.) of initially empty tank P was filled in 1 hour, when all 3 pipes were opened simultaneously? (Time taken by pipe C is 30 hours)

To find the volume of tank P filled in 1 hour when all three pipes are opened simultaneously, we need to determine the rate of work done by each pipe per hour.

Step 1: Calculate the rate of pipe A
From the given table, the time taken by pipe A to fill tank P is 10 hours.
Therefore, the rate at which pipe A fills the tank in 1 hour is:
$\text{Rate of A}=\frac{1}{10}$

Step 2: Calculate the rate of pipe B
We are given that the time taken by pipe C to empty the tank is 30 hours.
Therefore, the rate of pipe C to empty the tank is:
$\text{Rate of C}=\frac{1}{30}$
The ratio of the time taken by pipe B to fill tank P to that by pipe C to empty tank P is given as 2:3.
Let the time taken by pipe B be $T_B$ hours. We can set up the proportion:
$\frac{T_B}{30}=\frac{2}{3}$
Solving for $T_B$:
$T_B=\frac{2\times 30}{3}=20\text{hours}$
Therefore, the rate at which pipe B fills the tank in 1 hour is:
$\text{Rate of B}=\frac{1}{20}$

Step 3: Calculate the net fraction of the tank filled in 1 hour
When all three pipes are opened together, pipes A and B fill the tank while pipe C empties it. The net rate of filling in 1 hour is:
$\text{Net Rate}=\text{Rate of A}+\text{Rate of B}-\text{Rate of C}$
Substituting the rates:
$\text{Net Rate}=\frac{1}{10}+\frac{1}{20}-\frac{1}{30}$
Taking the Least Common Multiple (LCM) of 10, 20, and 30, which is 60:
$\text{Net Rate}=\frac{6+3-2}{60}=\frac{7}{60}$

Step 4: Calculate the volume of the tank filled in 1 hour
The total volume of tank P is given as 38,808 m³.
The volume filled in 1 hour is:
$\text{Volume Filled}=\frac{7}{60}\times 38808$
Performing the calculation:
$\text{Volume Filled}=7\times 646.8=4527.6{\text{m}}^3$
Rounding to the nearest integer, we get approximately 4528 m³.