Question

A cylindrical water tank of diameter $1.4$m and height $2.1$m is being fed by a pipe of diameter $3.5$cm through which water flows at the rate of $2m/s$.Calculate in minutes the time it takes to fill the tank.

Answer 1

Consider the cylindrical tank:

Diameter$=1.4$m

Radius$=r_1=\frac{1.4}{2}=0.7$m

Height $=h_1=2.1=\frac{21}{10}$m

Consider the cylindrical pipe:

Diameter$=3.5$cm$=\frac{35}{10}$cm$=\frac{7}{2}$cm

Radius$=r_2=\frac{7}{4}$cm$=\frac{7}{400}$m

Speed $=h_2=2m$per sec

$\therefore$ Time taken to fill the tank$=\frac{Volumeofcylindricaltank}{Volumeofcylindricalpipe}$

$=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

$=\frac{\pi \times \frac{7}{10}\times \frac{7}{10}\times \frac{21}{10}}{\pi \times \frac{7}{400}\times \frac{7}{400}\times 2}$

$=\frac{7}{10}\times \frac{7}{10}\times \frac{21}{10}\times \frac{400}{7}\times \frac{400}{7}\times \frac{1}{2}$

$=1680$secs

$=\frac{1680}{60}$minutes

$=28$minutes