A spherical water tank of radius, R = 4 meters is emptied through a small circular hole of radius r = 0.02 meters at the bottom. The top of the tank is open to atmosphere. The instantaneous water level, h, (measured from the bottom of the tank, at the drain), in the tank can be determined from the solution of the following ODE: dh dt = r² √2gh 2hR-h² where g = 9.81 m/s², t is in seconds and his in meters. a) If the initial water level (at t = 0 seconds) is h = 4m, find the water level of the tank after 3 hours, using Euler method with a step size of 1 hour (note: be consistent with the units). Give your answer correct to 4 decimal places. b) Based on your calculation in part (a), at least how many hours does it take to drain the water level below 2 meters? c) Use MATLAB's ode45 function to find the time it takes for the tank to drain completely (ie. h = 0). Give your answer in minutes, correct to the nearest 10 minutes (you need to use a step size of 10 minutes). Note: • you have to generate the full tspan vector (instead of just specifying the start and end values of the tspan), with a step size of 10 minutes and pass it to the ode45 function. • the height. h will become a complex value once it falls below 0 meters.