A rectangular water-tank measuring `80cm xx 60cm xx 60cm` is filled from a pipe of cross-sectional area `1.5cm^(2)`, the water emerging at 3.2 m/s. How long does it take to fill the tank?

Answer

To solve the problem of how long it takes to fill a rectangular water tank with the given dimensions and flow rate, we will follow these steps:

### Step 1: Calculate the Volume of the Tank
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given dimensions are:
- Length = 80 cm
- Breadth = 60 cm
- Height = 60 cm

Substituting the values:
\[ V = 80 \, \text{cm} \times 60 \, \text{cm} \times 60 \, \text{cm} \]
\[ V = 288000 \, \text{cm}^3 \]

### Step 2: Convert the Speed of Water to cm/s
The speed of water emerging from the pipe is given as 3.2 m/s. We need to convert this to cm/s:
\[ 3.2 \, \text{m/s} = 3.2 \times 100 \, \text{cm/s} = 320 \, \text{cm/s} \]

### Step 3: Calculate the Flow Rate
The flow rate \( Q \) can be calculated using the formula:
\[ Q = \text{speed} \times \text{cross-sectional area} \]
Given the cross-sectional area of the pipe is \( 1.5 \, \text{cm}^2 \):
\[ Q = 320 \, \text{cm/s} \times 1.5 \, \text{cm}^2 \]
\[ Q = 480 \, \text{cm}^3/\text{s} \]

### Step 4: Calculate the Time to Fill the Tank
The time \( t \) to fill the tank can be calculated using the formula:
\[ t = \frac{\text{Volume of the tank}}{\text{Flow rate}} \]
Substituting the values we found:
\[ t = \frac{288000 \, \text{cm}^3}{480 \, \text{cm}^3/\text{s}} \]
\[ t = 600 \, \text{s} \]

### Final Answer
The time required to fill the tank is **600 seconds**.

---