A cylindrical container is to be constructed having total volume 27 cubic feet. The sides are to be made of a special material that costs $2 per square foot, while the material for the top and bottom costs only $1 per square foot. What is the relationship between the radius r and the height h of the cheapest container that can be constructed according to these specifications?
A 10-foot latter is leaning against a vertical wall. At the moment that the angle between the ladder and the wall (at the top of the ladder) is p/3 radians, the bottom of the ladder is sliding away from the wall at a speed of 4 ft/sec. How fast, in radians per second, is the angle between the ladder and the wall increasing at that moment?
