PART 1:

A hemisphere of radius 22 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume. A woman pulls a sled which, together with its load, has a mass of m kg. Let g be the acceleration due to gravity. If her arm makes an angle of 0 with her body (assumed vertical) and the coefficient of friction (a positive constant) is , the least force, F, she must exert to move the sled is given by mgu F = sin 8 + u cos 0 If u = 0.12, find the maximum and minimum values of F for 0