An automated, swinging security light, hanging from the corner of a 35 ft tall building, is lighting the ground in front of the building. The angle 0 (see image below) is increasing at a rate of 0.6 radians per minute when the light on the ground is 50 ft away from the edge of the building. At that instant, what is the speed at which the light on the ground is traveling? Round to three decimal places. 35 ft 50 ft A spherical balloon is increasing in volume at a rate of 30 cm/min. At what rate is the radius increasing when the balloon has a volume of 80 cm? Round to the nearest 3rd decimal place. (Remember that the volume of a sphere is given by V = r). Bocky Rolboa finishes his morning jog strong by sprinting up the steps to the entrance of a national monument at 20 ft/sec. If the steps are angled 30 degrees above the horizontal, what is the rate at which his elevation is increasing? Water is exiting a giant cone shaped funnel at a rate of 15 cubic inches per second. The funnel is 75 inches high and has a maximum radius of 40 inches. What is the rate at which the water level of the funnel is changing when the water is 15 inches high? Note that the volume of a cone is V = rh.