Water flows at 3 metres per sec through a pipe of radius 4 cm. How many hours will it take to fill a tank 40 metres long, 30 metres broad and 8 metres deep, if the pipe remains full?

Options

A. 176.8 hours
B. 120 hour
C. 135.5 hours
D. None of these

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Convert the radius of the pipe from cm to meters
The radius of the pipe is given as 4 cm. We need to convert this to meters for consistency with the other measurements.

\[ \text{Radius in meters} = \frac{4 \text{ cm}}{100} = 0.04 \text{ m} \]

**Hint:** Remember that 1 cm = 0.01 m, so to convert cm to m, divide by 100.

### Step 2: Calculate the volume of water flowing through the pipe in 1 second
The volume \( V \) of a cylinder (the pipe) is given by the formula:

\[ V = \pi r^2 h \]

Where:
- \( r = 0.04 \text{ m} \) (radius of the pipe)
- \( h = 3 \text{ m} \) (height of water that flows in 1 second, which is the speed of water)

Calculating the volume:

\[ V = \pi (0.04)^2 (3) = \frac{22}{7} \times 0.0016 \times 3 \approx 0.0674 \text{ m}^3 \]

**Hint:** Use \( \pi \approx \frac{22}{7} \) for calculations, and remember to square the radius.

### Step 3: Calculate the volume of the tank
The volume \( V_t \) of the tank can be calculated using the formula for the volume of a cuboid:

\[ V_t = \text{length} \times \text{breadth} \times \text{height} \]

Where:
- Length = 40 m
- Breadth = 30 m
- Height = 8 m

Calculating the volume:

\[ V_t = 40 \times 30 \times 8 = 9600 \text{ m}^3 \]

**Hint:** Multiply the dimensions of the tank directly to find its volume.

### Step 4: Calculate the time taken to fill the tank
Now, we need to find out how many seconds it will take to fill the tank. We can find this by dividing the volume of the tank by the volume of water flowing through the pipe in one second.

\[ \text{Time (in seconds)} = \frac{V_t}{V} = \frac{9600}{0.0674} \approx 142,000 \text{ seconds} \]

**Hint:** When calculating time, remember that time is equal to total volume divided by flow rate.

### Step 5: Convert seconds to hours
To convert seconds to hours, we divide the total seconds by 3600 (since there are 3600 seconds in an hour).

\[ \text{Time (in hours)} = \frac{142,000}{3600} \approx 39.44 \text{ hours} \]

**Hint:** To convert seconds to hours, divide by 3600.

### Final Answer
It will take approximately **39.44 hours** to fill the tank.