Answer :

Let V be the volume of the cone, then


It is given that, h=


r = 6h


Therefore,


Now, the rate of change of its volume with respect to time (t) is given by:


Now, the rate of change of its volume with respect to x is as


……… by chain rule


…………….(1)


Now, it is also given that and h = 4cm


So, putting the value in equation (1), we get




Therefore, the height of the sand cone increasing when the height is 4 cm is cm/s.


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