Suppose that the tank in Example 7 is hemispherical, of radius R, initially full of water, and has an outlet of 5 cm² cross sectional area at the bottom. (Make a sketch.) Set up the model for outflow. Indicate what portion of your work in Example 7 you can use (so that it can become part of the general method independent of the shape of the tank). Find the time t to empty the tank (a) for any R, (b) for R = 1 m. Plot t as function of R. Find the time when h = R/2 (a) for any R, (b) for R = 1 m.