Question
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?
Answers
drwls
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]}
(dy/dt)*pi*(R^2-r^2) = (1 cm/s)*pi r^2
dy/dt = (1 cm/s)*{1/[(R/r)^2 -1]}