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AP Calculus Related Rates Formulas Flashcards

18 Questions

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AP Calculus Related Rates Formulas Flashcards

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Questions and Answers

What is the formula for the Area of a Circle?

A = 4πr^2

A = 2πr

A = πr^2 (correct)

A = πd^2

What is the formula for the Volume of a Cylinder?

V = 2πrh

V = πrh^2

V = π(r^2)h (correct)

V = (⅓)π(r^2)h

What is the Pythagorean Theorem?

(A^2) + (B^2) = 2C

(A^2) + (B^2) = (C^2) (correct)

(C^2) - (A^2) = (B^2)

(A + B)^2 = C^2

What is the formula for the Surface Area of a Cylinder?

S = 2πrh + 2π(r^2) Signup and view all the answers

What is the formula for the Area of a Square?

A = s^2 Signup and view all the answers

What is the formula for the Surface Area of a Sphere?

S = 4π(r^2) Signup and view all the answers

What is the formula for the Perimeter of a Rectangle?

P = 2l + 2w Signup and view all the answers

What is the formula for the Volume of a Cone?

V = (⅓)π(r^2)h Signup and view all the answers

What is the formula for the Volume of a Cube?

V = s^3 Signup and view all the answers

What is the formula for the Surface Area of a Cube?

S = 6(s^2) Signup and view all the answers

What is the equation of a Circle?

X^2 + Y^2 = R^2 Signup and view all the answers

What is the formula for the Circumference of a Circle?

C = 2πr Signup and view all the answers

What is the formula for the Volume of a Sphere?

V = (4/3)π(r^3) Signup and view all the answers

What is the alternative form of the Pythagorean Theorem?

L^2 + 6^2 = h^2 Signup and view all the answers

What is the formula for the Perimeter of a Square?

P = 4s Signup and view all the answers

What is the formula for the Area of a Rectangle?

A = lw Signup and view all the answers

What is the formula for the Area of a Triangle?

A = (1/2)bh Signup and view all the answers

What is the formula for the Area of an Equilateral Triangle?

A = (s^2√(3))/4 Signup and view all the answers

Study Notes

Formulas for Area and Volume

Area of a Circle: ( A = \pi r^2 )
Volume of a Cylinder: ( V = \pi (r^2)h )
Volume of a Cone: ( V = \frac{1}{3} \pi (r^2)h )
Volume of a Cube: ( V = s^3 )
Volume of a Sphere: ( V = \frac{4}{3} \pi (r^3) )

Geometric Properties

Pythagorean Theorem: ( A^2 + B^2 = C^2 )
Equation of a Circle: ( X^2 + Y^2 = R^2 )
Area of a Square: ( A = s^2 )
Area of a Rectangle: ( A = lw )
Area of a Triangle: ( A = \frac{1}{2}bh )
Area of an Equilateral Triangle: ( A = \frac{s^2 \sqrt{3}}{4} )

Surface Areas and Circumferences

Surface Area of a Cylinder: ( S = 2\pi rh + 2\pi(r^2) )
Surface Area of a Sphere: ( S = 6(s^2) ) (This is incorrect; the correct formula is ( S = 4\pi(r^2) ))
Circumference of a Circle: ( C = 2\pi r )

Perimeters

Perimeter of a Rectangle: ( P = 2l + 2w )
Perimeter of a Square: ( P = 4s )

Alternative Forms

Alternative Pythagorean Theorem: ( L^2 + 6^2 = h^2 )

These formulas and definitions serve as fundamental tools for solving problems related to area, volume, and geometric properties in calculus and geometry.

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Description

Test your knowledge of essential formulas related to area, volume, and surface area in this AP Calculus flashcard quiz. Each flashcard presents a formula along with its definition, helping you grasp the concepts needed for related rates problems. Perfect for quick revision before your exams!