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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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