Question

A right circular cylindrical tank of 9 metres height is filled with water. Water comes out from there through a pipe having length of 6 cm diameter with a speed of 225 metre per minute and the tank becomes empty after 2 hours 24 minutes. Calculate the length of radius of the tank.

Answer 1

Let the radius of the base of the tank be r metres.
`:.` the volume of the tank (i.e., of the water )
`=(22)/(7)xx r^(2)xx9` cubic.metres `= (198r^(2))/(7)` cubic.metres
Again , ` 6 cm = (6)/(100) m = 0.06` metre.
`:.` the volume of water comes out per minute
`=(22)/(7)xx((0.06)/(2))^(2)xx 225` cubic.metres
`=(22)/(7)xx0.03xx0.03xx225` cubic.metres `= (4.455)/(7)` cubic.metres.
2 hours 24 minutes `= (2xx60+24)` minutes `= 144` minutes
`:.` the volume of water comes out in 2 hours 24 minutes `= (4.455)/(7)xx144` cubic. metres
As per condition given, `(198r^(2))/(7)=(4.455)/(7)xx144` or, `r^(2) = (4.455)/(198)xx144` or, `r^(2) = 0.0225xx144`
or, ` r = sqrt(0.0225xx144)= 0.15xx12=1.8`
Hence the length of radius `= 1.8m = 1.8xx 100cm = 180 cm` .