A cone of radius r centimeters and height h centimeters is lowered point first in at a rate of 1 cm/s into a tall cylinder of radius R centimeters that is partially filled with water. How fast is the water level rising at instant the cone is completely submerged?

Answer 1

At that instant the water level stops rising. Prior to that, the water level rose at a steadily increasing rate dy/dt such that

(dy/dt)*pi*(R^2-r^2) = (1 cm/s)*pi r^2

dy/dt = (1 cm/s)*{1/[(R/r)^2 -1]}