Sand is pouring from a pipe at the rate of 12 `c m^3//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 4cm ?

Explanation

`h=1/6r`

`r=6h`

`(dv)/dt=12(cm^3)/s`

`(dh)/dt=?`

`v=(1/3pir^2h)`

`v=(h)`

`=1/3pi(6h)^2h`

`=(36pih^3)/3`

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