Calculus on Demand at Dartmouth College Lecture 27 | Index | Lecture 29
Lecture 28


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In this lecture we solve word problems involving variables that are linked through an equation that relates their rates of change.

Quick Question

If the radius of a circle is increasing at a rate of 2 m/s, how fast is the area growing when the radius equals 4 meters?



Related Rates

Today's Homework

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Related Rates Quiz


  • Click to see the exampleSuppose that an inflating balloon is spherical in shape, and its radius is changing at the rate of 3 centimeters per second. At what rate is the volume changing when the radius is 10 centimeters?
  • Click to see the exampleA baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square. If a pitcher throws a baseball at 100 miles per hour, how fast is the distance between the ball and first base changing as the ball crosses home plate?
  • Click to see the exampleA ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1 foot per second, how fast is the top of the ladder moving down when the bottom of the ladder is 8 feet from the wall?
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  • click to see the videoA balloon is being inflated at 1 ft3/min. At what rate is the radius increasing when the radius = 1 ft? 4 ft?
  • click to see the videoA 6 foot man walks away from an 18-foot lamp post. At what rate does his shadow lengthen if he walks 10 feet per minute?

Lecture 27 | Index | Lecture 29