(Originais Teachy 2024) - Question Medium of Mathematics

Consider a water reservoir in the shape of a right circular cone, and a field study that requires determining the volume of water stored in the reservoir. For this, it is assumed that the volume of a cone is given by the formula V = 1/3 π r^2 h, where V is the volume, r is the radius of the base, and h is the height of the cone. Knowing that the maximum storage capacity of the reservoir is 5000 liters and that the rate of change of the water level in the reservoir is 10 centimeters per hour, determine: (1) The rate of change of the water level in the reservoir in liters per hour. (2) If it is desired to increase the storage capacity of the reservoir to 6000 liters, by how many meters should the height of the cone be increased, keeping the same radius? Explain the steps of your reasoning and present a detailed calculation for each item.