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To solve this problem, we need to determine how much the water level in a cylindrical tank drops after 616 liters are drawn out.

### Step 1: Understanding the formula for the volume of a cylinder
The volume \( V \) of a cylinder is given by:

\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder (or the water level),
- \( \pi \) is a constant, approximately equal to 3.14159 (or \( \frac{22}{7} \) in this case).

### Step 2: Convert the volume drawn out into cubic centimeters
Since 1 liter = 1000 cubic centimeters (\( cm^3 \)), 616 liters is:

\[
616 \times 1000 = 616000 \, cm^3
\]

### Step 3: Use the volume formula to find the drop in height
The volume of water drawn out is equal to the base area of the cylinder multiplied by the height drop \( h \):

\[
\text{Volume} = \pi r^2 h
\]

Given:
- \( \text{Volume} = 616000 \, cm^3 \),
- \( r = 14 \, cm \),
- \( \pi = \frac{22}{7} \).

Substituting the values into the equation:

\[
616000 = \frac{22}{7} \times (14)^2 \times h
\]

### Step 4: Solve for \( h \)

First, calculate \( r^2 \):

\[
14^2 = 196
\]

Now, substitute:

\[
616000 = \frac{22}{7} \times 196 \times h
\]

Simplify:

\[
616000 = \frac{22 \times 196}{7} \times h = 616 \times 22 \times h = 13552 h
\]

Now, solve for \( h \):

\[
h = \frac{616000}{13552} = 45.45 \, cm
\]

Convert to meters:

\[
h = 0.4545 \, m
\]

Since the closest given option is 10 meters, the correct answer seems to be **Option D (10 meters)**. However, there is a mismatch, and this value doesn't directly align with the options provided, indicating that the correct assumption might involve some additional context or verification. 

Would you like further clarification, or do you want to dive into more details?

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Here are some related questions:
1. How do we calculate the volume of a cylinder for different units?
2. What is the impact of using a different value for \( \pi \) on the result?
3. How does the radius affect the water level drop when a fixed volume is removed?
4. Can you generalize this process for different shaped tanks?
5. What is the relationship between volume and surface area in cylindrical tanks?

**Tip:** Always check the units involved to ensure correct volume and height conversions when working with real-world objects like tanks!

A cylindrical tank of radius 14 cm is full of water. If 616 liters of water are drawn out, then the water level in the tank is dropped by _____ m. (Take π = 22/7)

Learn how to calculate the water level drop in a cylindrical tank with radius 14 cm when 616 liters of water are drawn out. This problem involves understanding the volume formula V = πr²h and unit conversions. Suitable for students in Grades 9-10.

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