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 t

Explanation

`h=frac{1}{6} r`


`r=6 h`


`frac{d v}{d t}=12 frac{{cm}^{3}}{{s}}`


`frac{d h}{d t}=` ?


`v=(frac{1}{3} pi r^{2} h)`


`v=(h)`


`=frac{1}{3} pi(6 h)^{2} h`


`=frac{36 pi h^{3}}{3}`


...