A rectangular water reservoir is 15 m by 12 m at the base. Water flows into it through a pipe whose cross-section is 5 cm by 3 cm at the rate of 16 m per second. Find the height ot which the water will rise in the reservoir in 25 minutes :

Options

A. 0.2 m
B. 2 cm
C. 0.5 cm
D. none of these

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the volume of water flowing into the reservoir in 25 minutes.

1. **Convert the dimensions of the pipe from centimeters to meters:**
- The cross-section of the pipe is given as 5 cm by 3 cm.
- Convert to meters:
- Width = 5 cm = 5/100 m = 0.05 m
- Height = 3 cm = 3/100 m = 0.03 m

2. **Calculate the cross-sectional area of the pipe:**
\[ \text{Area} = \text{Width} \times \text{Height} = 0.05 \, \text{m} \times 0.03 \, \text{m} = 0.0015 \, \text{m}^2 \]

3. **Calculate the volume of water flowing through the pipe per second:**
\[ \text{Volume per second} = \text{Area} \times \text{Flow rate} = 0.0015 \, \text{m}^2 \times 16 \, \text{m/s} = 0.024 \, \text{m}^3/\text{s} \]

4. **Calculate the total volume of water flowing in 25 minutes:**
- Convert 25 minutes to seconds:
\[ 25 \, \text{minutes} = 25 \times 60 = 1500 \, \text{seconds} \]
- Total volume:
\[ \text{Total Volume} = \text{Volume per second} \times \text{Total time} = 0.024 \, \text{m}^3/\text{s} \times 1500 \, \text{s} = 36 \, \text{m}^3 \]

### Step 2: Calculate the height to which the water will rise in the reservoir.

1. **Calculate the base area of the reservoir:**
\[ \text{Base Area} = \text{Length} \times \text{Width} = 15 \, \text{m} \times 12 \, \text{m} = 180 \, \text{m}^2 \]

2. **Use the volume of water to find the height:**
\[ \text{Height} = \frac{\text{Volume}}{\text{Base Area}} = \frac{36 \, \text{m}^3}{180 \, \text{m}^2} = 0.2 \, \text{m} \]

### Final Answer:
The height to which the water will rise in the reservoir is **0.2 meters**.

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