A container in the shape of an inverted cone has height 16 cm and radius 5 cm at the top It is partially filled with a liquid that oozes through the sides at a rate proportional to the area of the container that is in contact with the liquid (The surface area of a cone is rl, where r is the radius and l is the slant height ) If we pour the liquid into the container at a rate of 2cm3 min, then the height of the liquid decreases at a rate of 0 3 cm min when the height is 10 cm, if our goal is to keep the liquid at a constant height of 10 cm, at what rate should we pour the liquid into the container

Question: A container in the shape of an inverted cone has height 16 cm and radius 5 cm at the top. It is partially filled with

A container in the shape of an inverted cone has height 16 cm and radius 5 cm at the top. It is partially filled with a liquid that oozes through the sides at a rate proportional to the area of the container that is in contact with the liquid. (The surface area of a cone is πrl, where r is the radius and l is the slant height.) If we pour the liquid into the container at a rate of 2cm3/min, then the height of the liquid decreases at a rate of 0.3 cm/min when the height is 10 cm, if our goal is to keep the liquid at a constant height of 10 cm, at what rate should we pour the liquid into the container?

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