A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by :
(use `pi = (22)/(7)`)

Options

A. `10(1)/(2) cm`
B. `12(6)/(7) cm`
C. 14 cm
D. `11(3)/(7) cm`

Answer

To find out how much the water level in a cylindrical tank drops when 11 liters of water is drawn off, we can follow these steps:

### Step 1: Convert liters to cubic centimeters
Since the volume of water drawn off is given in liters and we need to work in cubic centimeters, we first convert liters to cubic centimeters.

1 liter = 1000 cubic centimeters, so:
\[ 11 \text{ liters} = 11 \times 1000 = 11000 \text{ cm}^3 \]

### Step 2: Calculate the radius of the tank
The diameter of the cylindrical tank is given as 35 cm. The radius (r) is half of the diameter:
\[ r = \frac{35}{2} = 17.5 \text{ cm} \]

### Step 3: Use the formula for the volume of a cylinder
The volume (V) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Where:
- \( \pi = \frac{22}{7} \)
- \( r \) is the radius
- \( h \) is the height of the water level

### Step 4: Set up the equation for the volume of water removed
We know that the volume of water removed is equal to the volume of the cylinder that corresponds to the height drop (h):
\[ 11000 = \pi r^2 h \]
Substituting the values we have:
\[ 11000 = \frac{22}{7} \times (17.5)^2 \times h \]

### Step 5: Calculate \( (17.5)^2 \)
Calculating \( (17.5)^2 \):
\[ (17.5)^2 = 306.25 \]

### Step 6: Substitute and solve for h
Now substituting back into the equation:
\[ 11000 = \frac{22}{7} \times 306.25 \times h \]
To simplify:
\[ 11000 = \frac{22 \times 306.25}{7} \times h \]
Calculating \( \frac{22 \times 306.25}{7} \):
\[ \frac{22 \times 306.25}{7} = \frac{6747.5}{7} = 964.07 \text{ (approximately)} \]
Now we can solve for \( h \):
\[ h = \frac{11000}{964.07} \approx 11.42 \text{ cm} \]

### Step 7: Final Calculation
To find the exact height drop:
\[ h = \frac{11000 \times 7}{22 \times 306.25} \]
Calculating:
\[ h = \frac{77000}{6747.5} \approx 11.42 \text{ cm} \]

### Conclusion
The water level in the tank will drop by approximately **11.42 cm**.

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