A hollow cone of base radius 10cm and height 10cm is held with its vertex downwards. The cone is initially empty when water is poured into it at the rate of (4pie) cm^3/s. Find the rate of increase in the depth of the water in the cone 18 second after pouring has commenced.

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Answer 1

at t=18, v=18*4π = 32π cm^3
since r=h,
v = 1/3 π r^2 h = π/3 h^3
so, when v=32π, h= ∛96

dv/dt = πh^2 dh/dt
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