A cylindrical tank of diameter 35 cm is completely filled with water. If 11 liters of water is taken out from the tank, then how much will the level of the tank decrease?

Question

Accepted Answer

To determine how much the water level in the cylindrical tank decreases when 11 liters of water is removed, we need to calculate the change in height of the water column.

1. **Volume of Water Removed**:  
   The volume of water removed is given as 11 liters. Since 1 liter is equivalent to 1000 cubic centimeters (cm³), 11 liters is equal to 11,000 cm³.

2. **Dimensions of the Cylinder**:  
   The diameter of the cylindrical tank is 35 cm, which means the radius $ r $ is half of the diameter:  
   $$ r = \frac{35}{2} = 17.5 \text{ cm} $$

3. **Formula for Volume of a Cylinder**:  
   The volume $ V $ of a cylinder is given by the formula:  
   $$ V = \pi r^2 h $$  
   where $ r $ is the radius and $ h $ is the height.

4. **Calculate the Decrease in Height**:  
   We need to find the decrease in height $ \Delta h $ when 11,000 cm³ of water is removed. Using the formula for volume:  
   $$ 11,000 = \pi (17.5)^2 \Delta h $$  
   Solving for $ \Delta h $:  
   $$ \Delta h = \frac{11,000}{\pi (17.5)^2} $$

5. **Perform the Calculation**:  
   $$ \Delta h = \frac{11,000}{3.14159 \times 306.25} $$  
   $$ \Delta h = \frac{11,000}{962.1125} $$  
   $$ \Delta h \approx 11.428 \text{ cm} $$

Thus, the level of the tank decreases by approximately 11.428 cm when 11 liters of water is removed. Therefore, Option 3 is the correct answer.

**Explanation for Incorrect Options**:

- **Option 1 (9.428 cm)**: This value is too low. The calculation shows that the decrease in height is greater than 9.428 cm, as derived from the volume formula.

- **Option 2 (10.428 cm)**: This value is also too low. The precise calculation indicates a decrease of approximately 11.428 cm, which is more than 10.428 cm.

- **Option 4 (12.428 cm)**: This value is too high. The calculated decrease in height is approximately 11.428 cm, which is less than 12.428 cm.

In conclusion, the correct decrease in the water level is 11.428 cm, making Option 3 the correct choice.