Question 1 Figure 1 shows a spherical tank for storing water. The tank is filled through a hole in the top and drained through a hole in the bottom. If the tank's radius is r, you can use integration to show that the volume of water in the tank as a function of its height h is given by 3 Figure 1-Draining of a spherical tank Torricelli's principle states that the liquid flow rate through the hole is proportional to the square root of the height h. Further studies in fluid mechanics have identified the relation more precisely, and the result is that the volume ow rate through the hole is given by where A is the area of the hole, g is the acceleration due to gravity, and Cd is an experimentally determined value that depends partly on the type of liquid. For water, C0.6 is a common value. We can use the principle of conservation of mass to obtain a differential equation for the height h Applied to this tank, the principle says that the rate of change of liquid volume in the tank must equal the flow rate out of the tank; that is, dV -=-q dt Use MATLAB to solve this equation using symbolic and numerical techniques to determine how long t will take for the tank to empty if the initial height is 9 m. The tank has a radius of 5 m and has a 1 cm-diameter hole in the bottom. Use g 9.81 m/sec2