Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

Dear

V= ∏/3 r²h

given h=r/6

  or  r=6h

V = 12∏h³

differentiate w.r.t time

dV/dt = 36∏h² dh/dt

dh/dt = 12/(36*∏*16)

        =6.63 X 10^-3 cm/sec

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