A cylindrical tank of diameter $35 \text{ cm}$ is full of water. If $11 \text{ litres}$ of water is drawn off, the water level in the tank will drop by

### Concept & Unit Conversion The volume of water drawn off equals the volume of the cylindrical section that represents the drop in water level. We must equate the drawn-off volume to a cylinder of the same diameter and unknown height. $$1 \text{ Litre} = 1000 \text{ cm}^3$$ ### Step-by-Step Solution 1. **Convert the drawn-off volume to cubic centimeters:** - Volume $V = 11 \text{ litres} = 11 \times 1000 = 11000 \text{ cm}^3$. 2. **Identify the cylinder's parameters:** - Diameter $d = 35 \text{ cm}$ $\Rightarrow$ Radius $r = \frac{35}{2} \text{ cm}$. - Let the drop in water level be $h$. 3. **Set up the volume equation:** - $V = \pi r^2 h$ - $11000 = \frac{22}{7} \times \left(\frac{35}{2}\right)^2 \times h$ - $11000 = \frac{22}{7} \times \frac{1225}{4} \times h$ 4. **Solve for $h$:** - $11000 = 22 \times 175 \times \frac{1}{4} \times h$ - $11000 = 962.5 \times h$ - $h = \frac{11000}{962.5} = \frac{110000}{9625}$ - Simplify by dividing by $25$: $\frac{4400}{385}$ - Simplify by dividing by $5$: $\frac{880}{77}$ - Simplify by dividing by $11$: $\frac{80}{7}$ - Convert to a mixed fraction: $h = 11 \frac{3}{7} \text{ cm}$ ### Exam Strategy & Shortcut Set up the cancellation directly: $h = \frac{11000 \times 7 \times 4}{22 \times 35 \times 35}$. Cancel $11$ from $22$ and $11000$ to get $1000$ and $2$. Cancel $7$ from $35$ to get $5$. The math condenses rapidly without needing large intermediate multiplications like $962.5$. ### Common Pitfall Failing to convert liters to cubic centimeters ($1000 \text{ cm}^3 = 1 \text{ L}$) will result in mismatched units and a drastically incorrect answer. ### Final Answer Therefore, the correct answer is **$11 \frac{3}{7} \text{ cm}$**.