How fast is the water level rising when the water is 3 cm deep (at its deepest point) if water is poured into a conical container at the rate of 10 cm3/sec. the cone points directly down, and it has a height of 25 cm and a base radius of 15 cm?
1 Answer
Given the rate of change in volume with respect to time is
We are looking for the rate of change in height with respect to time:
The obvious replacement for
The volume of a cone is given by the formula:
The ratio of the radius to the height for the given cone is
or
So, for the given cone:
Therefore
at h=3