Suppose that the tank is Example 5 is hemispherical, of radius R, initially full of water, and

Question:

Suppose that the tank is Example 5 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 5 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 = 1m. Plot t as function of R. Fine the time when h = R/2 (a) for any R, (b) for R = 1m.