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3.5a Related Rates
Related Rates:
An equation that relates two or more variables and their corresponding rates of change over time.
The Chain Rule is VERY IMPORTANT for this!!!
What is the equation that compares the change in volume of a sphere with the change in radius?
Examples:
1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the
distance s between the airplane and the radar station is decreasing at a rate of 400 km/hour when s = 10
km, what is the horizontal speed of the plane?
Draw it first!
2. Part 1: A snowball is melting at a rate of 2 cubic cm per min. If it remains spherical, at what rate is the
radius changing when the radius of the snowball is 5 cm?
Part 2: At what rate is the surface area changing when the radius is 5 cm
3. A 6 ft tall person is walking away from a 30 ft tall lamppost at a rate of 8 ft/sec. Assume the scenario
can be modeled with right triangles. At what rate is the length of the person’s shadow changing when
the person is 12 ft from the lamppost?
4. A ladder 10 meters long is leaning against a vertical wall with its other end on the ground. The top end
of the ladder is sliding down the wall. When the top end is 6 meters from the ground it is sliding down at
2m/sec. How fast is the bottom moving away from the wall at this instant?
Homework: Related Rates worksheet #4-6