A cylindrical tank of diameter 14 cm is full of water. If 9 litres of water is drawn off, the water level in the tank will drop bya)230.6 cmb)223.5 cmc)233.8 cmd)238.3 cme)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
Diameter of cylindrical tank = 14 cm
Volume of water drawn off = 9 litres

To find:
The drop in water level in the tank

Formula:
The volume of a cylinder = πr²h, where r is the radius and h is the height.

Calculation:
1. Convert the volume of water drawn off from litres to cubic centimeters:
1 liter = 1000 cubic centimeters
So, 9 litres = 9 * 1000 = 9000 cubic centimeters

2. Find the radius of the cylindrical tank:
The diameter of the tank is given as 14 cm.
Radius (r) = Diameter / 2 = 14 / 2 = 7 cm

3. Let the initial water level in the tank be h1 and the final water level after drawing off 9 litres of water be h2.

4. The initial volume of water in the tank = πr²h1
The final volume of water in the tank = πr²h2

5. According to the problem, the initial volume of water in the tank is equal to the final volume plus the volume of water drawn off:
πr²h1 = πr²h2 + 9000

6. Since the tank has a constant cross-sectional area, we can cancel out the πr² terms:
h1 = h2 + 9000

7. We are asked to find the drop in water level, which is the difference between the initial and final water levels:
Drop in water level = h1 - h2 = (h2 + 9000) - h2 = 9000

8. Therefore, the drop in water level in the tank is 9000 cm or 233.8 cm.

Hence, the correct answer is option (c) 233.8 cm.

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