1. Chapter 3, Section 8
Related Rates
Rita Korsunsky

3. 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

4. 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

5. 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

6. 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

7. 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 = ?