Section 4.6
Related Rates
• Consider the following problem:
– A spherical balloon of radius r centimeters has a volume
3
given by
V  (4 / 3)r
• Find dV/dr when r = 1 and when r = 2 and give a practical
interpretation of your answers.
• Suppose that the balloon is being inflated in such a way that r(t)
= 2t centimeters after t seconds. How fast is the volume of the
balloon increasing when r = 1? When r = 2?
• Air is being blown in the balloon at a constant rate of 50 cubic
centimeters per second. How fast is the radius of the balloon
increasing when r = 1? When r = 2?
A ladder 10 feet long rests against a vertical
wall. If the bottom of the ladder slides away
from the wall at a rate of 1 ft/s, how fast is the
top of the ladder sliding down the wall when
the bottom of the ladder is 6 ft from the wall?
A water tank has the shape of an inverted
circular cone with base radius 2m and height
4m. If water is being pumped into the tank at a
rate of 2m3/min, find the rate at which the
water level is rising when the water is 3m
deep.