Find the height up to

, fixed point iteration, reached by cubic meter of water stored in a spherical tank of radius meter. First prove all the hypothesis of the theorem, then perform the iterations. (Hint: First note that the sphere will be less than half full. The volume of the bottom meters of a hemisphere of radius is

which can be written as .

Note that ).

Find the height up to 10-4, fixed point iteration, reached by V = 1 cubic meter of water stored in a spherical tank of radius R = 1 meter. First prove all the hypothesis of the theorem, then perform the iterations. (Hint: First note that the sphere will be less than half full. The volume of the bottom H meters of a hemisphere of radius R is V = TtH?(R - H) which can be written as H =, TE(3R-H) Note that 0 SH S1). 3V