Question

If a pipe drained the water from a semi-spherical tank filled with water at the rate of $3 \dfrac{4}{7}$ litres per second, how much time will the pipe take to drain half of the water of the tank if the diameter of the tank is 3 m?

Hint:

Always convert all measurements into consistent units before calculation (metres to litres or cm³ to litres) and use the correct geometric formula for volume.

Answer 1

Step 1: Given data.
Diameter of the tank $= 3 \, \text{m}$
Radius $r = \frac{3}{2} = 1.5 \, \text{m}$
Rate of draining water $= 3 \dfrac{4}{7} = \frac{25}{7} \, \text{litres per second}$
We have to find the time to drain half of the tank. Step 2: Volume of a hemisphere.
\[ V = \frac{2}{3}\pi r^3 \] Substitute $r = 1.5 \, \text{m} = 150 \, \text{cm}$: Convert volume into litres. 1 m³ = 1000 litres. \[ V = \frac{2}{3}\pi (1.5)^3 = \frac{2}{3} \times 3.14 \times 3.375 = 7.07 \, \text{m}^3 \] \[ V = 7.07 \times 1000 = 7070 \, \text{litres} \] Step 3: Half of the volume.
\[ \text{Half volume} = \frac{7070}{2} = 3535 \, \text{litres} \]
Step 4: Find the time to drain.
\[ \text{Rate} = \frac{25}{7} \, \text{litres/second} \] \[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} = \frac{3535}{\frac{25}{7}} = 3535 \times \frac{7}{25} = 990.8 \, \text{seconds} \] \[ \text{Time} = \frac{990.8}{60} = 16.5 \, \text{minutes (approx.)} \]
Step 5: Conclusion.
\[ \boxed{\text{Time required} = 16.5 \, \text{minutes (approx.)}} \]