Archimedes (ca. 287-212 B. C.) was able to use clever geometric means to determine the relative volumes of a cylinder and the cone and paraboloid that would fit snugly into it (1800 years before Newton and Leibniz). With calculus, you don't have to be a genius to reach the same conclusions. (a) Determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius:

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?