A hemispherical bowl of radius 6cm contains water which is flowing into it at a constant rate.When the height of the water is h cm the volume V of water in the bowl is given by V=22/7(6h^2-1/3h^3)cm^3.Find the rate at which the water level is rising when h=3,given that the time taken to fill the bowl is 1minute.

Question

A hemispherical bowl of radius 6cm contains water which is flowing into it at a constant rate.When the height of the water is h cm the volume V of water in the bowl is given by V=22/7(6h^2-1/3h^3)cm^3.Find the rate at which the water level is rising when h=3,given that the time taken to fill the bowl is 1minute.                                                     
dV/dh=22/7

bobpursley · Answer

Why can't you just put the subject in the subject box? Otherwise, the right folks will never look at it.

VV=PI(6h^2-1/3h^3)
dV/dt=PI(12h - h^2)dh/dt

solve for dh/dt when h=3, and

v(h=6)=dv/dt * 60 sec or
dv/dt=PI (6*6^2-1/3 *6^3)/30 in cm^3/sec

Solomon · Answer

A hemispherical bowl of radius 6cm contains water which is flowing into it at a constant rate.when the height of the water is h cm, the volume v of the water in the bowl is given by v=π(6h^2-1/3h^3)cm^3.find the rate at which the water level is rising when h=3, given that the time taken to fill the bowl is one minute