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 m³s¹. Find the rate at which the water level is rising when the depth of the water is (x + k) 3.