The height of the water - level when the water of a right circular cone - shaped bottle of radius r unit and of height h unit is poured into a right circular cylinder shaped pot of radius mr unit will be

Options

A. `h/2m^(2)` unit
B. `(2h)/m` unit
C. `h/(3m^(2))` unit
D. `m/(2h)` unit

Answer

C

Explanation

The radius of the conical bottle = r unit and height = h unit
` :. ` the volume of the bottle ` = 1/3 pi^(2) h ` cubic - unit
Again , the radius of the cylindrical pot = mr unit
` :. ` the volume of the water poured into the pot ` = pi xx (mr)^(2) xx x` cubic - unit
` :. pi (mr)^(2) x = 1/3 r^(2) h `
` rArr m^(2) r^(2) x = (r^(2)h)/3`
` rArr x = h/(3m^(2))`
` :. ` the water - level of the pot will rise `h/(3m^(2))` unit .