Water flows through a cylindrical pipe, whose radius is 7 cm, at 5 metre per second. The time, it takes to fill an empty water tank, with height 1.54 metres and area of the base `(3 xx 5)` square metres, is (take `pi = (22)/(7)`)

Options

A. 6 minutes
B. 5 minutes
C. 10 minutes
D. 9 minutes

Answer

To solve the problem, we need to find out how long it takes to fill a water tank using the flow from a cylindrical pipe. Here’s how we can do it step by step:

### Step 1: Calculate the Volume of the Tank
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Given:
- Base Area = \( 3 \, \text{m} \times 5 \, \text{m} = 15 \, \text{m}^2 \)
- Height = \( 1.54 \, \text{m} \)

Now, substituting the values:
\[ V = 15 \, \text{m}^2 \times 1.54 \, \text{m} = 23.1 \, \text{m}^3 \]

### Step 2: Calculate the Volume of Water Flowing Through the Pipe in One Second
The volume \( V \) of water flowing through a cylindrical pipe per second can be calculated using the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the pipe in meters.
- \( h \) is the height (or length) of the water column flowing in one second, which is the speed of water flow.

Given:
- Radius \( r = 7 \, \text{cm} = 0.07 \, \text{m} \)
- Speed \( h = 5 \, \text{m/s} \)

Now, substituting the values:
\[ V = \frac{22}{7} \times (0.07)^2 \times 5 \]
Calculating \( (0.07)^2 \):
\[ (0.07)^2 = 0.0049 \]
Now substituting this value:
\[ V = \frac{22}{7} \times 0.0049 \times 5 \]
Calculating \( \frac{22}{7} \times 0.0049 \):
\[ \frac{22 \times 0.0049}{7} = \frac{0.1078}{7} \approx 0.0154 \]
Now multiplying by 5:
\[ V \approx 0.0154 \times 5 = 0.077 \, \text{m}^3 \]

### Step 3: Calculate the Time to Fill the Tank
To find the time \( T \) it takes to fill the tank, we can use the formula:
\[ T = \frac{\text{Volume of the tank}}{\text{Volume flow rate}} \]
Substituting the values:
\[ T = \frac{23.1 \, \text{m}^3}{0.077 \, \text{m}^3/s} \]
Calculating:
\[ T \approx 300 \, \text{seconds} \]

### Final Answer
The time it takes to fill the empty water tank is approximately **300 seconds**.

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