Question

A hemispherical tank of radius 3 cm is full of milk. It is connected to a pipe, through which liquid is emptied at the rate of $\frac{1}{7}$ litre per second. The time taken to empty the tank completely is:
[Assume $\pi =\frac{22}{7}$]

• A. 0.302 sec
• B. 0.396 sec
• C. 0.453 sec
• D. 0.492 sec

Answer 1

The correct option is B 0.396 sec

Radius of the hemisphere, r = 3 cm.

Volume of milk in the sphere $=\frac{2}{3}\times \pi \times r^3$
$=\frac{2}{3}\pi \times 3^3=\frac{22}{7}\times 2\times 3^{2}c{m}^3$
$=\frac{22}{7}\times 2\times 3^2\times \frac{1}{1000}litre$
Flow of liquid through the pipe $=\frac{1}{7}litrepersecond$
Time taken to empty the hemisphere
$=\frac{Volumeofmilk}{Flowrate}$
$=\frac{22}{7}\times 2\times 3^2\times \frac{1}{1000}\times 7=\frac{396}{1000}sec$