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 throught which water flowes at the rate of 2 metre per second. In how much time the tank will be filled ?

Answer 1

Diameter of cylindrical tank = 1.4 m

$\therefore$ Radius (r) = $\frac{1.4}{2}$ = 0.7 m

and height (h) = 2.1 m

$\therefore$ Volume of water in the tank = $\pi r^2$ h

=$\frac{22}{7}\times 0.7\times 0.7\times 2.1m^3$ = 3.234 $m^3$ Diameter of the tap = 3.5 cm

$\therefore Radius=\frac{3.5}{2}$ = 1.75 cm

Rate of flow of water in the pipe = 2 m/s

$\therefore$ Volume of water flow in 1 second = $\pi r^2$ h =

$\frac{22}{7}\times 1.75\times 1.75\times 200c{m}^3$

=$\frac{22}{7}\times \frac{175}{100}\times \frac{175}{100}\times 200c{m}^3$

=$\frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 200c{m}^3=1925c{m}^3$

$\therefore$ Time taken to fill the tank

=$\frac{3.234\times 100\times 100\times 100}{1925}sec$

=$\frac{3.234\times 100\times 100\times 100}{1000\times \times 1925}sec$.

= 1680 sec.

=$\frac{1680}{60}=28$ minutes