AP Calculus 2.12 – Related Rates I Formulas You Must Know! V Areaof base Distancebetweenbases = × Similar Triangles Ratios of corresponding sides are equal.

a) Find the rate at which the volume of the bubble is increasing when the radius of the bubble reaches 8cm . b) Determine the rate at which the volume of the ...

A rate of change is given by a derivative: If y = f(t), then dy dt. (meaning the derivative of y) gives the (instantaneous) rate at which y is changing with ...

Lesson 15: Related Rates. Important Formulas: Area of a Square: A = s². Area of a Circle: A = πг². Circumference of a Circle: C. = 2πη. Surface Area of a Cube: ...

In most related rates problems, we have an equation that relates a bunch of quantities that are changing over time.

The Pythagorean Theorem: a2 + b2 = c2. • The area and circumference of a circle: A = πr2,. C = 2πr. • The surface area and volume of a sphere: A = 4πr2,.

Any equation involving two or more variables that are differentiable functions of time t can be used to find an equation that relates their corresponding rates.

TO SOLVE: Use the relationship between variables, implicit differentiation and the chain rule, and the known derivative of our other variable with respect to ...

Note: Formulas for volume, surface area, etc., are inside the front cover of your text. Situation: Two or more quantities vary with time and are related by ...

This chapter concerns a type of derivative problem in which we solve for one rate of change, given that we know some other rate of change.