Math
posted by Marney on .
If a hemispherical bowl of radius 6cm contains water to a depth of h cm, the volume of the water is 1/3πh^2(18h). Water is poured into the bowl at a rate 4 cm^3/s . Find the rate at ehich the water level is rising when the depth is 2 cm.

V = (1/3)πh^2 (18h)
= 6πh^2  (1/3)πh^3
dV/dt = 12πh dh/dt  πh^2 dh/dt
4 = dh/dt(12πh  πh^2)
when h = 2
4 = dh/dt(24π  4π)
dh/dt = 4/(20π) = 1/(5π) cm/s