A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of the hemisphere fits exactly to the base of the cone and the height of the cone is 6 times thr radius of its base.
(a) Illustrate this information in a diagram.
(b) If the volume of the reservoir is \(333\frac{1}{3}\pi m^{3}\), calculate, correct to the nearest whole number, the :
(I) volume of the hemisphere ; (II) Total surface area of the reservoir. [Take \(\pi = \frac{22}{7}\)].