1. Suppose a snowball is melting and the radius is shrinking. lfthc volume ofthe snowball shrinks at the rate of dV/dt = -2 (cubic inches per hour). How fast is the radius changing when the radius is 1/2 inch? 2. A spherical balloon is losing air at the rate of2 cubic inches per minute. How fast is the radius ofthe balloon shrinking when the radius is 8 inches? 3. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 milesZ/hr. How fast is the radius on the spill increasing when the radius is 9 miles? 4. 'A weather balloon rising from the ground at 140 ft/min is tracked by a range nder located 500 feet from the point of liftoff. A. Find the rate at which the angle of inclination from the range nder to the balloon is changing when the balloon is 500 feet above the ground. B. Find the rate at which the straight-line distance to the balloon is changing when the balloon is 500 feet above the ground. 5. Let A be the area ofa square with sides that are length x and assume it varies with time. At a certain instant in time, the sides are 3 feet long and growing at a rate of2 ft/min. How fast is the area of the square growing at that instant in time? 6. A 13 foot long ladder is leaning against a wall. lfthe top of the ladder slips down the wall at a rate of 2 ft/sec., how fast will the base be moving away from the wall when the top of the ladder is 5 feet above the ground? 7. Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases a 5 ft/min, at what rate is the sand pouring from the chute when the pile is 10 feet high? 8. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At what rate must the air be released from the balloon when the radius is 9 cm? 9. A conical water tank that is placed vertex down has a radius of 10 feet at the top and is 24 feet high. If water lows in the tank at a rate of 20 cubic feet / minute, how fast is the depth of the water increasing when the water is 16 feet deep? 10. How fast does the water level drop when a cylindrical tank is drained at a rate of 3 liters / sec? 1 1. A highway patrol plane flies 1 mile above a straight road at a steady ground speed of 120 mph. The pilot sees an oncoming car and, with radar, determines that the line of sight distance from the plane to the car is 1.5 miles, decreasing at a rate of 136 mph. What is the car's speed along the highway