Chapter 3, Section 8 Related Rates Rita Korsunsky

Example 1: How fast does the radius of a spherical soap bubble change at the moment when radius is 1cm if the air is blown into it at the rate of 10 cm3/sec? Given: 1.Draw diagram 2.Write down what is given and what is asked for 3.Write the equation that relates the variables. 4 Implicitly differentiate 5.Plug in known values from ”Given” 6.Find values that are not directly given and plug them in too. 7.Find the unknown rate of change r

Example 2: How fast does the water level drop when a cylindrical tank with the radius 1 m is drained at the rate of 3 m3/sec? Given: h r=1

Example 3: A ladder 26 feet long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 4 ft/sec. How fast is the top sliding down the wall when the foot is 10 ft from the wall? Given: L = 26 y x 4 ft/sec When x = 10

Ex. 4. Water runs into a conical tank at the rate of 2 ft3/min Ex.4.Water runs into a conical tank at the rate of 2 ft3/min. The tank stands point down and has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft deep? Given: 5 ft x y 10 ft

Ex 5:A balloon rising from the ground at 140 ft/min is tracked by a rangefinder at point A, located 500 ft from the point of liftoff. Find the rate at which the angle at A and the range r are changing when the balloon is 500 ft above the ground. 140 ft/min r y 500 ft  A x Given: dy/dt = 140 ft/min y = 500 ft x = 500 ft d/dt = ? dr/dt = ?