The Total solution for NCERT class 6-12
Sand is pouring from a pipe at the rate of12 cm3/s. The falling sand forms a cone on the ground in such away 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?
The volume of a cone (V) withradius (r) and height (h) is given by,
It is given that,
The rate of change of volume with respect totime (t) is given by,
[By chain rule]
It is also given that
Therefore, when h = 4 cm,we have:
Hence, when the height ofthe sand cone is 4 cm, its height is increasing at the rate of