Question
Class 12MathematicsApplication of Derivatives
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?
Verified Answer
The volume of a cone (V) with radius (r) and height (h) is given by,
y – yo = f’ (xo) (x -xo)
It is given that,
y = f(x)
(xo, yo)
The rate of change of volume with respect to time (t) is given by,
