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# 4.6 - 4.6 Related Rates What is a Rate of Change Formulas...

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Calculus Section 4.6 Page 26 4.6 Related Rates What is a Rate of Change? Formulas: Area: The radius r and area A of a circle are related by the equation A = π r 2 . Write an equation that relates dA dt to dr dt . The side s and area A of a square are related by the equation A = s 2 . Write an equation that relates dA dt to ds dt . Volume: The radius r and volume V of a sphere are related by the equation A = 4 3 π r 3 . Write an equation that relates dV dt to dr dt . Example 1 A balloon is filled with air. What is the relationship between the rate of change of volume and the rate of change of radius.

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Calculus Section 4.6 Page27 Example 2 What is the rate of increase of the volume of a balloon when the radius is 3 cm and the radius is increasing at a constant rate of 2 cm/sec. Example 3 The radius of a circular disk is increasing at the rate of 3 cm/sec. What is the rate at which the area is changing when the radius is 4?
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