An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm3/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?

First find the total height of the cone using similar triangles. Since current oil surface has radius 6 cm (from πr² = 36π) and is 3 cm from top, and top radius is 9 cm, we get total height = 9 cm. Current oil height from vertex = 6 cm, giving volume = (1/3)π(6²)(6) = 72π cm³. At drain rate of 1 cm³/hour, time = 72π hours.