Water flows at a speed of 10 m per minute through a right circular pipe of diameter 5 mm . In how much time a tank of conical shape having diameter 40 cm and depth 24 cm will be fulfilled completely by this pipe ?

Explanation

The diameter of the coniacal tank = 40 cm
` :.` its radius ` = 40/2 ` cm = 20 cm
The depth of the tank = 24 cm
` :. ` the volume of the tank ` = 1/3 xx pixx (20)^(2) xx 24 ` cc
` = 1/3 xx pi xx 20 xx 20 xx 4 ` cc
= 3200 `pi` cc
Let the tank will be fulfilled completely in x - minute
` :. ` the length of the water - column = 10 x metres = 1000 x cm
Clearly the length of the cylindrical water - column is 100 x cm
and its radius = `5/2 ` mm = `5/(2 xx 10) ` cm = 1/4 cm
` :. ` the volume of cylindrical water - column ` = pi xx (1/4)^(2) xx 1000 x ` cc
` pi xx 1/16 xx 1000 ` cc
As per question , ` (pixx 1000x)/16 = 3200 pi `

` rArr x = (3200 xx 16)/1000 = 256/5 = 51 1/5`
Hence the tank will be completely fulfilled in `51 1/5` minutes