A right circular cone is held with its apex facing downwards and is inscribed in a sphere with fixed radius k cm within the interval 1 cm ≤ k ≤ 5 cm and the distance from the base of the cone to the center of the sphere is x cm. a. Evaluate the maximum volume of the cone by assigning k to a value within the given interval. Discuss the difference of use between the first derivative test and second derivative test to optimize the volume. b.Water is poured into the cone at a rate of 10 m3s−1. Find the rate at which the water level is rising when the depth of the water is (x + k) − 3.

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