1. A spherical star has a diameter of 100 x 106 km (100,000,000 km) across. When it collapses, the diameter shrinks at a rate of 70 km/s. At the beginning of the collapse, how fast is the star losing volume, in km3/s? You may leave your answer in exact form, using scientific notation, or a decimal approximation 2. A boat is being pulled into a dock by a winch which is 10 ft above sea level. The rope is being pulled into the winch at a rate of 4 ft/min. At the moment that the rope is 50.5 ft: a) How fast is the boat approaching the dock? b) How fast is the angle changing between the rope and sea level (in rad/min or degrees/min)? 3. The volume of an inflatable ball is increasing at a constant rate of 4318 cubic feet per minute. At the instant when the volume of the sphere is 1204 cubic feet, what is the rate of change of the surface area of the ball? The volume of a sphere can be found with the equation V = 4/3 r3 and the surface area can be found with S=4r2. Round your answer to three decimal places (if necessary)