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

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# Contents

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? Answer

Related Rates

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### Quiz

Related Rates Quiz

### Examples

• Suppose 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?
• A 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?
• A 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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### Videos

Lecture 27 | Index | Lecture 29