An inverted cone with height 10cm and radius 2cm is partially filled with liquid which is oozing out through the sides at a rate proportional to the area of the cone in contact with the liquid. (The area of a cone is pi rl where r is the radius and l is the slant height of the cone) Liquid is also being poured in to the top of the cone at a rate of 1 cubic cm/min. At what rate must liquid be poured into the top of the cone to keep the liquid at a constant depth of 4cm?

Question