Dr. Hurtubise expects his students to become proficient with algebra. However, he also recognizes that many applied problems cannot be solved without some sort of numerical routine. Although many of the problems found in calculus textbooks are contrived so that the equations have easy algebraic solutions, equations which come from applied problems are often impossible to solve algebraically. Dr. Hurtubise expects his students to learn to recognize which problems can be solved algebraically and which problems require a numerical solution. He expects his students to use a graphing calculator to obtain numerical solutions to those problems which cannot be solved algebraically.
A grain silo consists of a cylindrical main section, with height 30 ft, and a hemispherical roof. In order to achieve a total volume of 15,000 ft^3 (including the part inside the roof section), what should the radius of the silo be?
Suppose that you have a gasoline tank in the shape of a cylinder lying on its side. If the gas tank is 27 inches in diameter, how deep is the gas in the tank when the tank is 1/4 full?
A cow is tied to a silo with radius r by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow.