Question

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes.

Answer 1

Diameter of pipe = 2 cm

$\therefore$ Radius(r) = $\frac{2}{2}=1cm=0.01m$

Length of flow of water in 1 second= 6 m

$\therefore$ Length of flow in 30 minutes

$=6\times 30\times 60m=10800m$

$\therefore$ Volume of water $=\pi r^{2}h$

$=\frac{22}{7}\times 0.01\times 0.01\times 10800m^3$

=$\frac{22}{100}\times \frac{1}{100}\times 10800=\frac{2376}{700}{m}^3$=

$\therefore$ Volume of water in tank = $\frac{2376}{700}{m}^3$

Radius of the base of tank(R) = 60 cm

$=\frac{6}{10}m$

Let rise of water = $h_1$

$\therefore$ Volume of water = $\pi R^2{h}_1$

$=\frac{22}{7}\times \frac{6}{10}\times \frac{6}{10}\times h_1$

$\therefore \frac{792}{700}{h}_1=\frac{2376}{700}$

$\therefore$ Rise of water= 3 m