MAC 2311C Lecture Notes - Lecture 5: Rade People

To solve a related rates problem, follow the steps: 1. Sketch a diagram if possible. 2. Write down all the variables along with the rates given. 3. Write down the equation that relates all the variables. 4. Differentiate the equation implicitly. 5. Solve for the unknown rate.

1. Suppose a spherical balloon is inflated at the rate of 10 cubic centimeters per minute. How fast is the radius of the balloon increasing at the time when the radius is 5 cm? Recall that the formula for the volume of a sphere is V = 4/3 πr3.

2. A 20-foot ladder is leaning against the wall. If the base of the ladder is sliding away from the wall at the rate of 3 feet per second, find the rate at which the top of the ladder is sliding down when the top of the ladder is 8 feet from the ground.

3. Water leaking onto a floor creates a circular puddle with an area that increases at the rate of 3 square centimeters per minute. How fast is the radius of the puddle increasing when the radius is 10 cm? Recall that the formula for the area of a circle is A = r2π.